MathsCBSE Class 12 · Board exam 2025, set 65/1/1 · 2 marks · Very short answer

CBSE Class 12 Mathematics 2025: question 25(b)

Set in the CBSE Class 12 board exam of 2025, paper 65/1/1, section B, question 25(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(b) · 2 marks · Very short answerVector Algebra

Find a vector of magnitude 21 units in the direction opposite to that of $A B$ where A and B are the points A(2, 1, 3) and B(8, $- 1$ , 0) respectively.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 65/1/1.

Hints

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

Hint 1

The opposite direction to $A B$ is the direction of $B A$ .

Hint 2

Find the unit vector along $B A$ and multiply it by 21.

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.

The direction opposite to $A B$ is that of $B A$ : $B A = (2 - 8) \hat{i} + (1 + 1) \hat{j} + (3 - 0) \hat{k} = - 6 \hat{i} + 2 \hat{j} + 3 \hat{k}$ .
1 mark
Its magnitude is $∣ B A ∣ = 36 + 4 + 9 = 7$ . The required vector is $21 \times \frac{- 6 i ^ + 2 j ^ + 3 k ^}{7}$ .
½ mark
This simplifies to $3 (- 6 \hat{i} + 2 \hat{j} + 3 \hat{k}) = - 18 \hat{i} + 6 \hat{j} + 9 \hat{k}$ .
½ mark

Answer: $- 18 \hat{i} + 6 \hat{j} + 9 \hat{k}$

Where the marks are

Finds $B A = - 6 \hat{i} + 2 \hat{j} + 3 \hat{k}$ (1 mark)
Multiplies the unit vector by 21 (½ mark)
Gets $- 18 \hat{i} + 6 \hat{j} + 9 \hat{k}$ (½ mark)

Revise the chapter

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 paper2025 board paper, set 65/1/1: every question, by section.

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CBSE Class 12 Mathematics 2025: question 25(b)

Hints

Step-by-step solution

Revise the chapter

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