Mastering Vectors
Mathematics
GCSE Higher
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A worksheet covering Vectors for GCSE Higher students.
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Mastering Vectors
Subject: MathematicsGrade: GCSE Higher
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Date:
Untitled Worksheet
Grade GCSE Higher
A
Introduction
Review the basic concepts of vectors, including vector addition, subtraction, and scalar multiplication. Remember the key formula: |a| = √(a₁² + a₂²) for the magnitude of vector a = (a₁, a₂).
B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Given vectors A = (3, 4) and B = (1, -2), find A + B.
[2 marks]2.
Calculate the magnitude of vector C = (6, 8).
[2 marks]3.
Subtract vector D = (2, 5) from vector A = (7, 12).
[2 marks]4.
Multiply vector E = (3, -4) by scalar 2.
[2 marks]5.
If vector F = (x, y) has magnitude 13 and x = 5, find y.
[3 marks]6.
Determine whether vectors G = (4, 7) and H = (8, 14) are parallel.
[2 marks]7.
Find the scalar p such that vector P = p(2, -3) equals (8, -12).
[2 marks]8.
Calculate the dot product of vectors Q = (1, 2) and R = (3, 4).
[3 marks]9.
A point P has position vector (x, y). Find the coordinates of P if the vector from P to Q = (5, 7) is perpendicular to vector P = (x, y).
[4 marks]10.
Challenge: Two vectors have magnitudes 10 and 24, and their dot product is 120. Find the angle between them.
[4 marks]Quick Actions
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- Created
- 12/30/2025
- Updated
- 12/30/2025
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