A vector perpendicular to the vectors i+j and i-j is (A) -2j (B) 3k (C) 2i (D) 2i+k

MathsCBSE Class 12 · Sample paper, session 2026-27 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2026-27: question 15

From the official CBSE sample question paper for 2026-27, section A, question 15, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q15 · 1 mark · MCQVector Algebra

A vector perpendicular to the vectors $\hat{i} + \hat{j}$ and $\hat{i} - \hat{j}$ is

(A) $- 2 \hat{j}$
(B) $3 \hat{k}$
(C) $2 \hat{i}$
(D) $2 \hat{i} + \hat{k}$

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

Both given vectors lie in the XY-plane.

Hint 2

Find their cross product.

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.

$(\hat{i} + \hat{j}) \times (\hat{i} - \hat{j}) = - 2 \hat{k}$ , so any vector perpendicular to both is parallel to $\hat{k}$ .
Among the options, only $3 \hat{k}$ is parallel to $\hat{k}$ .
1 mark

Answer: Option (B)

Where the marks are

Recognises that the perpendicular vector is along $\hat{k}$ (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 15

Hints

Step-by-step solution

Revise the chapter

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