If a=4 i+6 j and b=3 j+4 k, then the vector form of the component of a along b is (A) 18/5(3 i+4 k) (B) 18/25(3 j+4 k) (C) 18/5(3 i+4 k) (D) 18/25(4 i+6 j)

MathsCBSE Class 12 · Sample paper, session 2023-24 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2023-24: question 12

From the official CBSE sample question paper for 2023-24, section A, question 12, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q12 · 1 mark · MCQVector Algebra

If $a = 4 \hat{i} + 6 \hat{j}$ and $b = 3 \hat{j} + 4 \hat{k}$ , then the vector form of the component of $a$ along $b$ is

(A) $\frac{18}{5} (3 \hat{i} + 4 \hat{k})$
(B) $\frac{18}{25} (3 \hat{j} + 4 \hat{k})$
(C) $\frac{18}{5} (3 \hat{i} + 4 \hat{k})$
(D) $\frac{18}{25} (4 \hat{i} + 6 \hat{j})$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

Open one hint at a time and try again before the next.

Hint 1

Find $a \cdot b$ first.

Hint 2

Projection vector $= \frac{a \cdot b}{∣ b ∣ ^{2}} b$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

$a \cdot b = 0 + 18 + 0 = 18$ and $∣ b ∣^{2} = 9 + 16 = 25$ .
Vector component of $a$ along $b$ $= \frac{a \cdot b}{∣ b ∣ ^{2}} b = \frac{18}{25} (3 \hat{j} + 4 \hat{k})$ : option (B).
1 mark

Answer: $\frac{18}{25} (3 \hat{j} + 4 \hat{k})$ , option (B)

Where the marks are

Uses $\frac{a \cdot b}{∣ b ∣ ^{2}} b$ correctly (1 mark)

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Chapter: Vector Algebra (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Vector Algebra, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24: every question, by section.

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CBSE Class 12 Mathematics sample paper 2023-24: question 12

Hints

Step-by-step solution

Revise the chapter

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