Vectors Practice Questions

KCSE (Kenya) · KCSE Mathematics · 148 free MCQs with instant results and detailed explanations.

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Sample Questions from Vectors

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Easy

What is the resultant of the vectors A = 3i + 4j and B = 1i - 2j?

A. 4i + 2j

B. 2i + 6j

C. 4i + 6j

D. 2i + 2j

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Correct Answer: A

To find the resultant, we add the corresponding components of vectors A and B: (3 + 1)i + (4 - 2)j = 4i + 2j.

Easy

If vector C = 5i - 3j represents a displacement, what is the magnitude of vector C?

A. √34

B. 34

C. 8

D. √30

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Correct Answer: A

The magnitude of vector C is calculated using the formula √(x^2 + y^2) = √(5^2 + (-3)^2) = √(25 + 9) = √34.

Easy

Which of the following statements about two vectors A and B is true if A = -2i + 3j and B = 2i + 3j?

A. A and B are equal.

B. A and B are opposite.

C. A and B are perpendicular.

D. A and B are in the same direction.

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Correct Answer: B

Vectors A and B are opposite because they have equal magnitudes but point in opposite directions for the i component, while their j components are the same.

Medium

If vector A = 2i - 3j and vector B = ki + 4j are orthogonal, what is the value of k?

A. -6/2

B. 6/2

C. 3/2

D. -4/2

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Correct Answer: A

For vectors to be orthogonal, their dot product must equal zero: (2)(k) + (-3)(4) = 0. This leads to 2k - 12 = 0, hence k = 6/2.

Medium

Vector A is represented as 5i + 7j and is reflected across the x-axis. What is the new vector R?

A. 5i - 7j

B. -5i + 7j

C. -5i - 7j

D. 7i + 5j

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Correct Answer: A

When a vector is reflected across the x-axis, only the j component changes sign. Therefore, R = 5i - 7j.

Medium

If vector A = 2i + 3j and vector B = 4i - j, which of the following represents the vector 2A - B?

A. 0i + 9j

B. -2i + 9j

C. 10i + 5j

D. 8i + j

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Correct Answer: B

Calculating 2A gives 4i + 6j. Now subtract B: (4i + 6j) - (4i - j) = 0i + 7j, resulting in 7j.

Medium

What is the resultant vector of the vectors A = 4i + 3j and B = -2i + 5j?

A. 2i + 8j

B. 6i + 2j

C. 2i + 2j

D. 2i + 5j

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Correct Answer: A

To find the resultant vector, we add the corresponding components of the vectors A and B. The i-components: 4 + (-2) = 2; the j-components: 3 + 5 = 8. Therefore, the resultant vector is 2i + 8j.

Hard

If vector C = 4i + 3j is rotated 90 degrees counterclockwise, what is the new vector C'?

A. -3i + 4j

B. 3i + 4j

C. 4i - 3j

D. -4i - 3j

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Correct Answer: A

Rotating a vector (x, y) by 90 degrees counterclockwise transforms it to (-y, x). For C = (4, 3), C' becomes (-3, 4), hence C' = -3i + 4j.

Hard

If vector A = 3i + 4j and vector B = 5i - 2j, what is the dot product of vectors A and B?

A. 7

B. 6

C. 26

D. 2

Show Answer & Explanation

Correct Answer: A

The dot product of two vectors A and B is calculated as A.B = Ax * Bx + Ay * By. Here, A.B = (3 * 5) + (4 * -2) = 15 - 8 = 7.

Q10

Hard

Given vectors P = 2i + 3j + k and Q = ai + bj + 4k, if P and Q are orthogonal, what is the value of a + b?

A. 1

B. 0

C. -1

D. 2

Show Answer & Explanation

Correct Answer: B

Vectors P and Q are orthogonal when their dot product is zero. The dot product gives 2a + 3b + 4 = 0. Setting a + b = 0 leads to a + b = -4, thus a + b = 0.

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Vectors — KCSE (Kenya) KCSE Mathematics Practice Questions Online

This page contains 148 practice MCQs for the chapter Vectors in KCSE (Kenya) KCSE Mathematics. The questions are organized by difficulty — 58 easy, 71 medium, 19 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.