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Vectors practice questions with answers

Foundation and Higher · Grade 5 · Non-calculator

A second set of vectors questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Add the vectors (0, 2) and (5, 1).

Show answer

Answer: (5, 3)

  1. x: 0 + 5 = 5.
  2. y: 2 + 1 = 3, vector is (5, 3).
  • Method (1): x: 0 + 5 = 5.
  • Accuracy (1): y: 2 + 1 = 3, vector is (5, 3).

Question 2 Easy

Add the vectors (4, 0) and (1, 3).

Show answer

Answer: (5, 3)

  1. x: 4 + 1 = 5.
  2. y: 0 + 3 = 3, vector is (5, 3).
  • Method (1): x: 4 + 1 = 5.
  • Accuracy (1): y: 0 + 3 = 3, vector is (5, 3).

Question 3 Medium

Multiply the vector (5, 1) by -1. Give the answer as a column vector.

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Answer: (-5, -1)

  1. Negate top: 5 × (-1) = -5.
  2. Negate bottom: 1 × (-1) = -1, vector is (-5, -1).
  • Method (1): Negate top: 5 × (-1) = -5.
  • Accuracy (1): Negate bottom: 1 × (-1) = -1, vector is (-5, -1).

Question 4 Medium

Subtract the vector (2, 1) from (5, 6).

Show answer

Answer: (3, 5)

  1. x: 5 - 2 = 3.
  2. y: 6 - 1 = 5, vector is (3, 5).
  • Method (1): x: 5 - 2 = 3.
  • Accuracy (1): y: 6 - 1 = 5, vector is (3, 5).

Question 5 Hard

Work out the column vector from (1, 1) to (4, 5).

Show answer

Answer: (3, 4)

  1. End minus start x: 4 - 1 = 3.
  2. End minus start y: 5 - 1 = 4, vector is (3, 4).
  • Method (1): End minus start x: 4 - 1 = 3.
  • Accuracy (1): End minus start y: 5 - 1 = 4, vector is (3, 4).

Question 6 Hard

Work out the column vector from (0, 0) to (3, 4).

Show answer

Answer: (3, 4)

  1. End minus start x: 3 - 0 = 3.
  2. End minus start y: 4 - 0 = 4, vector is (3, 4).
  • Method (1): End minus start x: 3 - 0 = 3.
  • Accuracy (1): End minus start y: 4 - 0 = 4, vector is (3, 4).

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

Work out the column vector from (1, 3) to (5, 7).

Show answer

Answer: (4, 4)

  1. Subtract start x from end x: 5 - 1 = 4.
  2. Subtract start y from end y: 7 - 3 = 4, giving (4, 4).
  • Method (1): End minus start for one component, e.g. 5 - 1 = 4
  • Accuracy (1): (4, 4)

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

How do you add two column vectors?

  1. Add corresponding top and bottom components
  2. Multiply top by top and bottom by bottom
  3. Add all four numbers into one scalar
Show answer

Add corresponding top and bottom components Component-wise addition: (a, b) + (c, d) = (a+c, b+d).

Check 2

What is (3, 1) + (2, 5)?

  1. (5, 6)
  2. (6, 5)
  3. (1, -4)
Show answer

(5, 6) 3+2 = 5 and 1+5 = 6.

Check 3

What is (1, 2) + (3, 4)?

  1. (4, 6)
  2. (3, 8)
  3. (4, 5)
Show answer

(4, 6) 1+3 = 4 and 2+4 = 6.

Check 4

What is 2 × (3, 4)?

  1. (6, 8)
  2. (5, 6)
  3. (6, 4)
Show answer

(6, 8) Multiply both components by 2.

Check 5

What is 3 × (2, 3)?

  1. (6, 9)
  2. (5, 6)
  3. (6, 3)
Show answer

(6, 9) Multiply both components by 3.

Check 6

What is -1 × (5, 1)?

  1. (-5, -1)
  2. (5, -1)
  3. (-5, 1)
Show answer

(-5, -1) Multiply both components by -1.

Check 7

What is (5, 6) - (2, 1)?

  1. (3, 5)
  2. (7, 7)
  3. (3, 7)
Show answer

(3, 5) 5 - 2 = 3 and 6 - 1 = 5.

Check 8

What is (1, 8) - (4, 2)?

  1. (-3, 6)
  2. (3, 6)
  3. (-3, 10)
Show answer

(-3, 6) 1 - 4 = -3 and 8 - 2 = 6.

Check 9

How do you find the vector from point A to point B?

  1. B - A (end minus start)
  2. A - B (start minus end)
  3. A + B
Show answer

B - A (end minus start) Vector AB = position of B minus position of A.

Check 10

What is the vector from (1, 2) to (4, 6)?

  1. (3, 4)
  2. (-3, -4)
  3. (5, 8)
Show answer

(3, 4) (4 - 1, 6 - 2) = (3, 4).

Check 11

What is the vector from (2, 5) to (6, 1)?

  1. (4, -4)
  2. (-4, 4)
  3. (8, 6)
Show answer

(4, -4) (6 - 2, 1 - 5) = (4, -4).

Check 12

What is the vector from (0, 0) to (3, 4)?

  1. (3, 4)
  2. (0, 0)
  3. (-3, -4)
Show answer

(3, 4) (3 - 0, 4 - 0) = (3, 4).

Check 13

What does the top number in a column vector represent?

  1. Horizontal movement (x-direction)
  2. Vertical movement (y-direction)
  3. Length of vector
Show answer

Horizontal movement (x-direction) The top component represents displacement along the x-axis.

Check 14

What does the bottom number in a column vector represent?

  1. Vertical movement (y-direction)
  2. Horizontal movement (x-direction)
  3. Angle of vector
Show answer

Vertical movement (y-direction) The bottom component represents displacement along the y-axis.

Check 15

If vector AB is (3, 4), what is the reverse vector BA?

  1. (-3, -4)
  2. (3, -4)
  3. (-3, 4)
Show answer

(-3, -4) Reversing direction negates both components: BA = -AB.

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