Vector equations – Hard (AS Level)

Last updated: 31/10/2021

A-Level Maths Vectors Vector equations – Hard (AS Level)

Time limit: 0

Quiz Summary

0 of 25 Questions completed

Questions:

Information

You have already completed the quiz before. Hence you can not start it again.

Quiz is loading…

You must sign in or sign up to start the quiz.

You must first complete the following:

Results

Quiz complete. Results are being recorded.

Results

0 of 25 Questions answered correctly

Your time:

Time has elapsed

You have reached 0 of 0 point(s), (0)

Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)

Average score
Your score

Categories

Not categorized 0%

Current
Review
Answered
Correct
Incorrect

Question 1 of 25

1. Question
A,B,C and D have position vectors:a = -6i+9jb = 8i+jc = -10i+9jd = -24i+17j Prove that ABCD is a parallelogram
- AB = 14i-8j and DC = 14i-8j BC = -18i+8j and AD = -18i+8j
- BC = -2i+10j and AD = -30i+26j
- $AB = 2 i + 10 j and DC = - 34 i + 26 j$
- $AB = 14 i - 8 j and DC = 14 i - 8 j$
Correct

Incorrect
Question 2 of 25

2. Question
A,B,C and D have position vectors:a = -9i+6jb = 5i-2jc = -8i+9jd = -22i+17j Prove that ABCD is a parallelogram
- $AB = 14 i - 8 j and DC = 14 i - 8 j BC = - 13 i + 11 j and AD = - 13 i + 11 j$
- $BC = - 13 i + 11 j and AD = - 13 i + 11 j$
- $BC = 3 i - 7 j and DA = 31 i - 23 j$
- $AB = 4 i - 4 j and DC = 30 i - 26 j BC = 3 i - 7 j and DA = 31 i - 23 j$
Correct

Incorrect
Question 3 of 25

3. Question
A,B,C and D have position vectors:a = -i-2jb = -6i-10jc = 5i-7jd = 10i+j Prove that ABCD is a parallelogram
- $AB = - 5 i - 8 j and DC = - 5 i - 8 j BC = 11 i + 3 j and AD = 11 i + 3 j$
- $BC = 11 i + 3 j and AD= 11 i + 3 j$
- $BC = i + 17 j and DA = - 9 i + j$
- $AB = 7 i + 12 j and DC = - 15 i + 6 j BC = i + 17 j and DA = - 9 i + j$
Correct

Incorrect
Question 4 of 25

4. Question
A,B,C and D have position vectors: a = -5i-4jb = -8i-10jc = 3i-7jd = 6i-j Prove that ABCD is a parallelogram
- $AB = - 3 i - 6 j and DC = - 3 i - 6 j BC = 11 i + 3 j and AD = 11 i + 3 j$
- $AB = 13 i + 14 j and DC = - 9 i + 8 j BC = 5 i + 17 j and AD = - i + 5 j$
- $BC = - 5 i - 17 j and DA = i - 5 j$
- $BC = 11 i + 3 j and DA = 11 i + 3 j$
Correct

Incorrect
Question 5 of 25

5. Question
A,B,C and D have position vectors:a = -i+3jb = 5i-8jc = i+9jd = -5i+20j Prove that ABCD is a parallelogram
- $AB = 6 i - 11 j and DC = 6 i - 11 j BC = - 4 i + 17 j and AD = - 4 i + 17 j$
- $BC = 6 i + j and AD = - 6 i + 23 j$
- $AB = 4 i - 5 j and DC = - 4 i + 29 j BC = 6 i + j and DA = - 6 i + 23 j$
- $AB = 6 i - 11 j and DC = 6 i - 11 j$
Correct

Incorrect
Question 6 of 25

6. Question
A,B,C and D have position vectors:a = 9i-3jb = 2i-8jc = 4i+6jd = 11i+11j Prove that ABCD is a parallelogram
- $AB = - 7 i - 5 j and DC = - 7 i - 5 j BC = 2 i + 14 j and AD = 2 i + 14 j$
- $AB = - 11 i + 11 j and DC = - 15 i - 17 j$
- $BC = 2 i + 14 j and AD = 2 i + 14 j$
- $AB = 11 i - 11 j and DC = 15 i + 17 j$
Correct

Incorrect
Question 7 of 25

7. Question
ABCD is a parallelogram.A,B and C have position vectors:a = 5i+7jb = 5i+6jc = -8i+3j Find the position vector of D
- $d = - 8 i + 4 j$
- $d = 18 i + 10 j$
- $d = 2 i + 16 j$
- $d = 8 i - 4 j$
Correct

Incorrect
Question 8 of 25

8. Question
ABCD is a parallelogram.A,B and C have position vectors:a = 2i-6jb = -2i+4jc = 5i+7j Find the position vector of D
- $d = 9 i - 3 j$
- $d = - 9 i + 3 j$
- $d = 5 i + 5 j$
- $d = - 5 i - 9 j$
Correct

Incorrect
Question 9 of 25

9. Question
ABCD is a parallelogram.A,B and C have position vectors:a = -8i-6jb = -i-8jc = 8i+8j Find the position vector of D
- $d = i + 10 j$
- $d = - i - 6 j$
- $d = - 17 i - 22 j$
- $d = - 17 i - 22 j$
Correct

Incorrect
Question 10 of 25

10. Question
ABCD is a parallelogram.A,B and C have position vectors:a = -i-3jb = i+9jc = 10i+7j Find the position vector of D
- $d = 8 i - 5 j$
- $d = - 8 i + 5 j$
- $d = - 10 i - j$
- $d = - 10 i - j$
Correct

Incorrect
Question 11 of 25

11. Question
ABCD is a parallelogram.A,B and C have position vectors:a = 9i+6jb = 2i-4jc = 5i-7j Find the position vector of D
- $d = 12 i + 3 j$
- $d = 6 i + 9 j$
- $d = 16 i - 5 j$
- $d = - 12 i - 3 j$
Correct

Incorrect
Question 12 of 25

12. Question
ABCD is a parallelogram.A,B and C have position vectors: a = -4i-4jb = -9i+2jc = -i-j Find the position vector of D
- $d = 4 i - 7 j$
- $d = - 4 i + 7 j$
- $d = - 14 i - 3 j$
- $d = - 12 i - j$
Correct

Incorrect
Question 13 of 25

13. Question
A,B and C have position vectors: a = i+3jb = -i+9jc = -4i+18j Prove that A,B and C are collinear.
- $AB = - 2 i + 6 j and BC = - 3 i + 9 j AB = 2 (- i + 3 j) and BC = 3 (- i + 3 j)$
- $AB = - 2 i + 6 j and BC = - 3 i + 9 j$
- $AB = + 6 j and BC = - 3 i + 12 j AB = 2 (+ 3 j) and BC = 3 (- i + 4 j)$
- $AB = - 2 i + 4 j and BC = - 6 i + 9 j AB = 2 (- i + 2 j) and BC = 3 (- 2 i + 3 j)$
Correct

Incorrect
Question 14 of 25

14. Question
A,B and C have position vectors:a = -i-jb = -4i+8j”c = -6i+14j Prove that A,B and C are collinear.
- $AB = - 3 i + 9 j and BC = - 2 i + 6 j AB = 3 (- i + 3 j) and BC = 2 (- i + 3 j)$
- $AB = - 3 i + 12 j and BC = + 6 j AB = 3 (- i + 4 j) and BC = 2 (+ 3 j)$
- $AB = + 9 j and BC = - 2 i + 8 j AB = 3 (+ 3 j) and BC = 2 (- i + 4 j)$
- $AB = - 6 i + 9 j and BC = - 2 i + 4 j AB = 3 (- 2 i + 3 j) and BC = 2 (- i + 2 j)$
Correct

Incorrect
Question 15 of 25

15. Question
A,B and C have position vectors:a = i-jb = -i+jc = -2i+2j Prove that A,B and C are collinear.
- $AB = - 2 i + 2 j and BC = - i + j AB = 2 (- i + j) and BC = (- i + j)$
- $AB = - 4 i and BC = - 2 i$
- $AB = + 2 j and BC = - i + 2 j AB = 2 (+ j) and BC = 1 (- i + 2 j)$
- $AB = - 2 i and BC = - 2 i + j AB = 2 (- i) and BC = 1 (- 2 i + j)$
Correct

Incorrect
Question 16 of 25

16. Question
A,B and C have position vectors:a = 2i+2jb = 4i-2jc = 5i-4j Prove that A,B and C are collinear.
- $AB = 2 i - 4 j and BC = i - 2 j AB = 2 (i - 2 j) and BC = (i - 2 j)$
- $AB = - 6 j and BC = - 3 j AB = 2 (- 3 j) and BC = 1 (- 3 j)$
- $AB = 2 i - 2 j and BC = 2 i - 2 j AB = 2 (i - j) and BC = 1 (2 i - 2 j)$
- $AB = 2 i - 4 j and BC = i - 2 j$
Correct

Incorrect
Question 17 of 25

17. Question
A,B and C have position vectors:a = 2i-jb = 4i-5jc = 7i-11j Prove that A,B and C are collinear.
- $AB = 2 i - 4 j and BC = 3 i - 6 j AB = 2 (i - 2 j) and BC = 3 (i - 2 j)$
- $AB = - 6 j and BC = - 9 j AB = 2 (- 3 j) and BC = 3 (- 3 j)$
- $AB = 2 i - 2 j and BC = 6 i - 6 j AB = 2 (i - j) and BC = 3 (2 i - 2 j)$
- $AB = 4 i - 4 j and BC = 3 i - 3 j AB = 2 (2 i - 2 j) and BC = 3 (i - j)$
Correct

Incorrect
Question 18 of 25

18. Question
A,B and C have position vectors: a = -i-2jb = -5ic = -7i+j Prove that A,B and C are collinear.
- $AB = - 4 i + 2 j and BC = - 2 i + j AB = 2 (- 2 i + j) and BC = (- 2 i + j)$
- $AB = - 4 i + 2 j and BC = - 2 i + j$
- $AB = - 2 i + 4 j and BC = - i + 2 j$
- $AB = - 4 i + 4 j and BC = - i + j AB = 2 (- 2 i + 2 j) and BC = 1 (- i + j)$
Correct

Incorrect
Question 19 of 25

19. Question
A,B and C are collinear .A and B have position vectors:a = -2i+10j and b = 8i+5jC is between A and B where AC:CB = 1:3 Find the position vector of C
- $c = \frac{1}{2} i + \frac{35}{4} j$
- $c = \frac{5}{2} i - \frac{5}{4} j$
- $c = 28 i - 5 j$
- $c = - \frac{9}{2} i + \frac{45}{4} j$
Correct

Incorrect
Question 20 of 25

20. Question
A,B and C are collinear. A and B have position vectors:a = 8i+3j and b = -i+8j C is between A and B where AC:CB = 2:1 Find the position vector of C
- $c = 2 i + \frac{19/}{3} j$
- $c = - 6 i + \frac{10/}{3} j$
- $c = 14 i - \frac{1}{3} j$
- $c = \frac{7}{2} i + \frac{11}{2} j$
Correct

Incorrect
Question 21 of 25

21. Question
A,B and C are collinear. A and B have position vectors:a = 6i+3j and b = -4i-7j C is between A and B where AC:CB = 3:2 Find the position vector of C
- $c = - 3 j$
- $c = - 4 i - 7 j$
- $c = - \frac{2}{3} i - \frac{11}{3} j$
- $c = 12 i + 9 j$
Correct

Incorrect
Question 22 of 25

22. Question
A,B and C are collinear. A and B have position vectors:a = 8i-6j and b = -7i-j C is between A and B where AC:CB = 1:2 Find the position vector of C
- $c = 3 i - \frac{13/}{3} j$
- $c = - 7 i - j$
- $c = 13 i - \frac{23}{3} j$
- $c = - 37 i + 9 j$
Correct

Incorrect
Question 23 of 25

23. Question
A,B and C are collinear. A and B have position vectors: a = -3i-7j and b = i-3j C is between A and B where AC:CB = 2:3 Find the position vector of C
- $c = - \frac{7/}{5} i - \frac{27/}{5} j$
- $c = 3 i - j$
- $c = 7 i + 3 j$
- $c = - \frac{23}{5} i - \frac{43}{5} j$
Correct

Incorrect
Question 24 of 25

24. Question
A,B and C are collinear. A and B have position vectors:a = 9i+j and b = -5i-6j C is between A and B where AC:CB = 1:1 Find the position vector of C
- $c = 2 i - \frac{5/}{2} j$
- $c = - 5 i - 6 j$
- $c = - 7 i - \frac{7}{2} j$
- $c = 16 i + \frac{9}{2} j$
Correct

Incorrect
Question 25 of 25

25. Question
A,B and C are collinear. A and B have position vectors:a = -8i+4j and b = 3i+6j C is between A and B where AC:CB = 3:2 Find the position vector of C
- $c = - \frac{7/}{5} i + \frac{26/}{5} j$
- $c = \frac{31}{3} i + \frac{22}{3} j$
- $c = \frac{17}{2} i + 7 j$
- $c = - \frac{2}{3} i + \frac{16}{3} j$
Correct

Incorrect