For two non-zero vectors a and b, a =√(6), a=1 and b=3i+4j-2k. Find b .

MathsCBSE Class 12 · Sample paper, session 2026-27 · 2 marks · Very short answer

CBSE Class 12 Mathematics sample paper 2026-27: question 24

From the official CBSE sample question paper for 2026-27, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerVector Algebra

For two non-zero vectors $a$ and $b$ , $∣ a ∣ = 6$ , $a \cdot b = 1$ and $b \times a = 3 \hat{i} + 4 \hat{j} - 2 \hat{k}$ . Find $∣ b ∣$ .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

The magnitude of $b \times a$ is the same as that of $a \times b$ .

Hint 2

Combine $∣ a ∣∣ b ∣ sin θ$ and $∣ a ∣∣ b ∣ cos θ$ using $sin^{2} θ + cos^{2} θ = 1$ .

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.

$∣ a \times b ∣ = ∣ b \times a ∣ = 3^{2} + 4^{2} + (- 2)^{2} = 29$
½ mark
Use the identity $∣ a \times b ∣^{2} + (a \cdot b)^{2} = ∣ a ∣^{2} ∣ b ∣^{2}$ [since $sin^{2} θ + cos^{2} θ = 1$ ].
½ mark
$29 + 1 = 6∣ b ∣^{2} \Rightarrow ∣ b ∣^{2} = 5 \Rightarrow ∣ b ∣ = 5$
1 mark

Answer: $∣ b ∣ = 5$

Where the marks are

Finds $∣ a \times b ∣ = 29$ (½ mark)
Uses Lagrange's identity (½ mark)
Obtains $∣ b ∣ = 5$ (1 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 paperSample paper 2026-27: every question, by section.

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CBSE Class 12 Mathematics sample paper 2026-27: question 24

Hints

Step-by-step solution

Revise the chapter

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