Vectors (representation and operations) — KCSE Mathematics

KCSE Mathematics · 117 practice questions · 4 syllabus objectives

37 easy40 medium40 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Represent a vector in column notation and as a directed line segment; find the magnitude of a vector using Pythagoras' theorem

Add, subtract and multiply vectors by a scalar; find the resultant vector and unit vector in the direction of a given vector

Apply position vectors to find the midpoint and a point dividing a line in a given ratio; prove collinearity

Vectors (representation and operations)

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easySHORT ANSWER2 marks

Define the scalar multiplication of vector u = column vector (3, 4) by 2 and state the resulting vector. (2 marks)

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Part (a) — 2 marks

Scalar multiplication involves multiplying each component of the vector by the scalar (1 mk)

The resulting vector is column vector (6, 8) (1 mk)

easySHORT ANSWER2 marks

Given vector v = column vector (6, 8), calculate the magnitude of vector v using Pythagoras' theorem. (2 marks)

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Part (a) — 2 marks

Apply Pythagoras' theorem: |v| = √(6² + 8²) (1 mk)

Correct value: |v| = 10 (1 mk)

easySHORT ANSWER2 marks

Given vector u represented as u = column vector (3, 4), express vector u as a directed line segment from the origin. (2 marks)

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Part (a) — 2 marks

The directed line segment from (0,0) to (3,4) (1 mk)

Direction indicated by the coordinates (3,4) (1 mk)

Let vectors p = (2, 5) and q = (4, 1). Find: (a) the unit vector in the direction of p [2 marks] (b) the resultant vector p + 3q [2 marks]

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