Further Maths – i and j Vectors (inc to find properties of geometric figures)

Last updated: 01/04/2020

Summer Start for A-Level Maths Vectors & Mechanics Further Maths – i and j Vectors (inc to find properties of geometric figures)

Question 1 of 45

1. Question
“p = ” 9i-8j” and q = “-5i-5j”Calculate p + q”
- 4i-13j
- 45i-40j
- $- 45 i + 40 j$
- $2 i - 2 j$
Correct

Incorrect
Question 2 of 45

2. Question
“p = “-6i+7j” and q = ” 9i-6j”Calculate p + q”
- $3 i + j$
- $15 i - 13 j$
- $- 54 i - 42 j$
- $54 i + 42 j$
Correct

Incorrect
Question 3 of 45

3. Question
“p = “-8i+9j” and q = “-3i-7j”Calculate p + q”
- $- 11 i + 2 j$
- $5 i - 16 j$
- $- 5 i + 16 j$
- $3 i - j$
Correct

Incorrect
Question 4 of 45

4. Question
“p = “-7i+4j” and q = “-2i-j”Calculate p – q”
- $- 5 i + 5 j$
- $14 i - 4 j$
- $9 i - 3 j$
- $- 14 i + 4 j$
Correct

Incorrect
Question 5 of 45

5. Question
“p = “-9i-6j” and q = ” i+5j”Calculate p – q”
- $- 10 i - 11 j$
- $- 9 i - j$
- $8 i + j$
- $- 9 i - 30 j$
Correct

Incorrect
Question 6 of 45

6. Question
“p = ” 5i+9j” and q = ” 8i-j”Calculate p – q”
- $- 3 i + 10 j$
- $- 40 i + 9 j$
- $40 i - 9 j$
- <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mi>i</mi><mo>+</mo><mn>9</mn><mi>j</mi></math>
Correct

Incorrect
Question 7 of 45

7. Question
“p = ” 5i-10j” and q = “-6i+j”Calculate p – q”
- $11 i - 11 j$
- $30 i + 10 j$
- $- 11 i + 11 j$
- <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mn>30</mn><mi>i</mi><mo>−</mo><mn>10</mn><mi>j</mi></math>
Correct

Incorrect
Question 8 of 45

8. Question
“p = ” 2i-8j”Calculate ” 4″p”
- $8 i - 32 j$
- $i - 2 j$
- $2 i + 12 j$
- $6 i - 4 j$
Correct

Incorrect
Question 9 of 45

9. Question
“p = “-i+5j”Calculate “-“p”
- $i - 5 j$
- $- 2 i + 4 j$
- $+ 6 j$
- $- i + 5 j$
Correct

Incorrect
Question 10 of 45

10. Question
“p = ” 7i+8j”Calculate ” 5″p”
- $35 i + 40 j$
- $- i - 2 j$
- $- 12 i - 13 j$
- $- 35 i - 40 j$
Correct

Incorrect
Question 11 of 45

11. Question
“p = ” 4i-8j”Calculate “-2″p”
- $- 8 i + 16 j$
- $- 2 i + 4 j$
- $- 6 i + 6 j$
- $- 2 i + 10 j$
Correct

Incorrect
Question 12 of 45

12. Question
“p = “-9i+4j” and q = ” 3i-6j”Calculate “-“p”+5″q”
- $24 i - 34 j$
- $- 6 i + 26 j$
- $- 24 i + 34 j$
- $6 i - 26 j$
Correct

Incorrect
Question 13 of 45

13. Question
“p = ” i-9j” and q = “-8i-4j”Calculate “-2″p”+5″q”
- $- 42 i - 2 j$
- $- 38 i - 38 j$
- $42 i + 2 j$
- $38 i + 38 j$
Correct

Incorrect
Question 14 of 45

14. Question
“p = “-4i-3j” and q = “-7i+9j”Calculate ” 5″p”+2″q”
- $- 34 i + 3 j$
- $34 i - 3 j$
- $- 6 i - 33 j$
- $6 i + 33 j$
Correct

Incorrect
Question 15 of 45

15. Question
“p = “-6i-8j” and q = “-3i+5j”Calculate “-4″p”+4″q”
- $12 i + 52 j$
- $36 i + 12 j$
- $- 12 i - 52 j$
- $- 36 i - 12 j$
Correct

Incorrect
Question 16 of 45

16. Question
“p = “-2i-4j”Calculate |p|”
- $4.47$
- 5.59
- 4.06
- 6.71
Correct

Incorrect
Question 17 of 45

17. Question
“p = ” 9i+4j”Calculate |p|”
- 9.85
- 8.95
- 14.77
- 10.87
Correct

Incorrect
Question 18 of 45

18. Question
“p = ” 7i-2j”Calculate |p|”
- 7.28
- 8.01
- 4.85
- 9.10
Correct

Incorrect
Question 19 of 45

19. Question
“p = ” i+9j” and q = “-4i+2j”Calculate |”-4″p”-2″q|”
- 40.20
- 36.55
- 44.22
- 26.80
Correct

Incorrect
Question 20 of 45

20. Question
“p = “-6i+2j” and q = “-8i+9j”Calculate |” 4″p”+4″q|”
- 71.22
- 47.48
- 88.03
- 106.83
Correct

Incorrect
Question 21 of 45

21. Question
“p = “-3i+2j” and q = “-6i-9j”Calculate |” 4″p”-2″q|”
- 26.00
- 39.00
- 28.60
- 32.50
Correct

Incorrect
Question 22 of 45

22. Question
“p = ” 7i+j” and q = ” 4i+j”Calculate |”-3″p”+5″q|”
- 2.24
- 2.80
- 3.36
- 2.04
Correct

Incorrect
Question 23 of 45

23. Question
“p = “-12i-16j”Calculate a vector parallel to p with magnitude ” 40
- $- 24 i - 32 j$
- $- 36 i - 48 j$
- $- 12 i - 16 j$
- $- 26 i - 34 j$
Correct

Incorrect
Question 24 of 45

24. Question
“p = ” 40i-30j”Calculate a vector parallel to p with magnitude ” 200
- $160 i - 120 j$
- $200 i - 150 j$
- $164 i - 116 j$
- $156 i - 124 j$
Correct

Incorrect
Question 25 of 45

25. Question
“p = “-28i+45j”Calculate a vector parallel to p with magnitude ” 212
- $- 112 i + 180 j$
- $- 140 i + 225 j$
- $- 108 i + 184 j$
- $- 84 i + 135 j$
Correct

Incorrect
Question 26 of 45

26. Question
“p = “-12i+9j”Calculate a vector parallel to p with magnitude ” 60
- $- 48 i + 36 j$
- $- 60 i + 45 j$
- $- 52 i + 32 j$
- $- 44 i + 40 j$
Correct

Incorrect
Question 27 of 45

27. Question
“p = “-40i-30j”Calculate the unit vector p̂”
- $- \frac{4}{5} i - \frac{3}{5} j$
- $\frac{1}{5} i - \frac{10}{17} j$
- $- \frac{41}{50} i - \frac{31}{50} j$
- $- \frac{39}{50} i - \frac{29}{50} j$
Correct

Incorrect
Question 28 of 45

28. Question
“p = ” 12i-5j”Calculate the unit vector p̂”
- $\frac{12}{13} i - \frac{5}{13} j$
- $- \frac{1}{13} i - \frac{5}{12} j$
- $i - \frac{4}{13} j$
- $\frac{11}{13} i - \frac{6}{13} j$
Correct

Incorrect
Question 29 of 45

29. Question
“p = ” 20i+21j”Calculate the unit vector p̂”
- $\frac{20}{29} i + \frac{21}{29} j$
- <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow class="MJX-TeXAtom-ORD"><mn>19</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mn>29</mn></mrow></mfrac></mrow><mi>i</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow class="MJX-TeXAtom-ORD"><mn>20</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mn>29</mn></mrow></mfrac></mrow><mi>j</mi></math>
- <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow class="MJX-TeXAtom-ORD"><mn>9</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mn>29</mn></mrow></mfrac></mrow><mi>i</mi><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow><mrow class="MJX-TeXAtom-ORD"><mn>4</mn></mrow></mfrac></mrow><mi>j</mi></math>
Correct

Incorrect
Question 30 of 45

30. Question
“p = “-36i-27j”Calculate the unit vector p̂”
- $- \frac{4}{5} i - \frac{3}{5} j$
- $- \frac{7}{9} i - \frac{26}{45} j$
- $\frac{1}{5} i - \frac{27}{46} j$
- $- \frac{37}{45} i - \frac{28}{45} j$
Correct

Incorrect
Question 31 of 45

31. Question
“A,B,C and D have position vectors:a = “-4i+8j”b = ” 2i-9j”c = ” 9i-8j”d = ” 3i+9j “Prove that ABCD is a parallelogram”
- $AB = 6 i - 17 j and DC = 6 i - 17 j BC = 7 i + j and DA = 7 i + j$
- $AB = 6 i - 17 j and DC = 6 i - 17 j$
- $BC = - 11 i + 17 j and DA = i - 17 j$
- $BC = 11 i - 17 j and DA = - i + 17 j$
Correct

Incorrect
Question 32 of 45

32. Question
“A,B,C and D have position vectors:a = “-i+7j”b = “-6i-7j”c = ” 4i+4j”d = ” 9i+18j”Prove that ABCD is a parallelogram”
- $AB = - 5 i - 14 j and DC = - 5 i - 14 j BC = 10 i + 11 j and DA = 10 i + 11 j$
- $BC = 2 i + 3 j and DA = - 8 i - 25 j$
- $AB = - 7 i and DC = 13 i + 22 j BC = - 2 i - 3 j and DA = 8 i + 25 j$
- $AB = 7 i and DC = - 13 i - 22 j BC = 2 i + 3 j and DA = - 8 i - 25 j$
Correct

Incorrect
Question 33 of 45

33. Question
“A,B,C and D have position vectors:a = ” 5i-5j”b = ” 2i-5j”c = ” 8i+4j”d = ” 11i+4j”Prove that ABCD is a parallelogram”
- $AB = - 3 i and DC = - 3 i BC = 6 i + 9 j and DA = 6 i + 9 j$
- $BC = 10 i - j and DA = 16 i - j$
- $AB = 7 i - 10 j and DC = 19 i + 8 j BC = 10 i - j and DA = 16 i - j$
- $AB = - 7 i + 10 j and DC = - 19 i - 8 j BC = - 10 i + j and DA = - 16 i + j$
Correct

Incorrect
Question 34 of 45

34. Question
“ABCD is a parallelogram.A,B and C have position vectors:a = “-7i+7j”b = “-8i-j”c = “-i+4j “Find the position vector of D “
- $d = 12 j$
- $d = - 14 i + 2 j$
- <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>d = </mtext><mo>−</mo><mn>14</mn><mi>i</mi><mo>+</mo><mn>2</mn><mi>j</mi></math>
- $d = - 16 i + 10 j$
Correct

Incorrect
Question 35 of 45

35. Question
“ABCD is a parallelogram.A,B and C have position vectors:a = ” 5i-7j”b = ” 10i-5j”c = “-9i-3j”Find the position vector of D “
- $d = - 14 i - 5 j$
- $d = 24 i - 9 j$
- $d = 24 i - 9 j$
- $d = 6 i - 15 j$
Correct

Incorrect
Question 36 of 45

36. Question
“ABCD is a parallelogram.A,B and C have position vectors:a = ” 8i-3j”b = ” 10i+j”c = “-10i+3j”Find the position vector of D “
- $d = - 12 i - j$
- $d = 28 i - 5 j$
- $d = 12 i + j$
- $d = 28 i - 5 j$
Correct

Incorrect
Question 37 of 45

37. Question
“ABCD is a parallelogram.A,B and C have position vectors:a = ” 8i-4j”b = ” 5i+8j”c = ” 8i+5j”Find the position vector of D “
- $d = 11 i - 7 j$
- $d = 5 i - j$
- $d = - 11 i + 7 j$
- $d = 5 i - j$
Correct

Incorrect
Question 38 of 45

38. Question
“A,B and C have position vectors:a = “-i-j”b = ” 5i-10j”c = ” 9i-16j”Prove that A,B and C are collinear.”
- $AB = 6 i - 9 j and BC = 4 i - 6 j AB = 3 (2 i - 3 j) and BC = 2 (2 i - 3 j)$
- $AB = 6 i - 9 j and BC = 4 i - 6 j$
- $AB = 3 i - 12 j and BC = 2 i - 8 j AB = 3 (i - 4 j) and BC = 2 (i - 4 j)$
- $AB = 9 i - 9 j and BC = 4 i - 4 j AB = 3 (3 i - 3 j) and BC = 2 (2 i - 2 j)$
Correct

Incorrect
Question 39 of 45

39. Question
“A,B and C have position vectors:a = “-i-3j”b = “-4j”c = ” 3i-7j”Prove that A,B and C are collinear.”
- $AB = i - j and BC = 3 i - 3 j AB = (i - j) and BC = 3 (i - j)$
- $AB = - j and BC = 3 i - 6 j AB = 1 (- j) and BC = 3 (i - 2 j)$
- $AB = 2 i and BC = 6 i AB = 1 (2 i) and BC = 3 (2 i)$
- $AB = 2 i - j and BC = 3 i AB = 1 (2 i - j) and BC = 3 (i)$
Correct

Incorrect
Question 40 of 45

40. Question
“A,B and C have position vectors:a = ” i+j”b = ” 3i-5j”c = ” 4i-8j”Prove that A,B and C are collinear.”
- $AB = 2 i - 6 j and BC = i - 3 j AB = 2 (i - 3 j) and BC = (i - 3 j)$
- $AB = - 8 j and BC = - 4 j AB = 2 (- 4 j) and BC = 1 (- 4 j)$
- $AB = - 8 j and BC = - 4 j$
- $AB = 2 i - 8 j and BC = - 3 j AB = 2 (i - 4 j) and BC = 1 (- 3 j)$
Correct

Incorrect
Question 41 of 45

41. Question
“A,B and C have position vectors:a = ” 2i-3j”b = ” 6i-5j”c = ” 12i-8j”Prove that A,B and C are collinear.”
- $AB = 4 i - 2 j and BC = 6 i - 3 j AB = 2 (2 i - j) and BC = 3 (2 i - j)$
- $AB = 2 i - 4 j and BC = 3 i - 6 j AB = 2 (i - 2 j) and BC = 3 (i - 2 j)$
- $AB = 6 i - 2 j and BC = 6 i AB = 2 (3 i - j) and BC = 3 (2 i)$
- $AB = 2 i - 4 j and BC = 3 i - 6 j$
Correct

Incorrect
Question 42 of 45

42. Question
“A,B and C are collinear.A and B have position vectors:a = “-5i+j” and b = ” 4i+3j”C is between A and B where AC:CB = ” 1:2″Find the position vector of C”
- $c = - 2 i + \frac{5}{3} j$
- $c = 4 i + 3 j$
- $c = - 8 i + \frac{1}{3} j$
- $c = 3 i + \frac{2}{3} j$
Correct

Incorrect
Question 43 of 45

43. Question
“A,B and C are collinear.A and B have position vectors:a = ” 2i-4j” and b = ” 2i+9j”C is between A and B where AC:CB = ” 3:2″Find the position vector of C”
- $c = 2 i + \frac{19}{5} j$
- $c = 2 i + 9 j$
- $c = 2 i + \frac{31}{2} j$
- $c = + \frac{39}{5} j$
Correct

Incorrect
Question 44 of 45

44. Question
“A,B and C are collinear.A and B have position vectors:a = “-7i+6j” and b = ” 3i+j”C is between A and B where AC:CB = ” 1:2″Find the position vector of C”
- $c = - \frac{11}{3} i + \frac{13}{3} j$
- $c = 13 i - 4 j$
- $c = \frac{10}{3} i - \frac{5}{3} j$
- $c = 3 i + j$
Correct

Incorrect
Question 45 of 45

45. Question
“A,B and C are collinear.A and B have position vectors:a = “-4i+9j” and b = ” 2i-2j”C is between A and B where AC:CB = ” 1:3″Find the position vector of C”
- $c = - \frac{5}{2} i + \frac{25}{4} j$
- $c = - 2 i + \frac{16}{3} j$
- $c = - \frac{11}{2} i + \frac{47}{4} j$
- $c = 20 i - 35 j$
Correct

Incorrect

Further Maths – i and j Vectors (inc to find properties of geometric figures)

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