MathsCBSE Class 12 · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 12 Mathematics sample paper 2025-26: question 25

From the official CBSE sample question paper for 2025-26, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerVector Algebra

The two vectors $\hat{i} + \hat{j} + \hat{k}$ and $3 \hat{i} - \hat{j} + 3 \hat{k}$ represent the two sides $O A$ and $O B$ , respectively of a $Δ O A B$ , where $O$ is the origin. The point $P$ lies on $A B$ such that $O P$ is a median. Find the area of the parallelogram formed by the two adjacent sides as $O A$ and $O P$ .

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

A median from O goes to the midpoint of AB; write $O P$ using the midpoint formula.

Hint 2

Area of a parallelogram is the magnitude of the cross product of its adjacent sides.

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.

P is the midpoint of AB, so $O P = \frac{1}{2} (O A + O B) = \frac{1}{2} (4 \hat{i} + 4 \hat{k}) = 2 \hat{i} + 2 \hat{k}$ .
½ mark
Area of parallelogram with adjacent sides OA, OP $= ∣ O A \times O P ∣$ .
½ mark
$O A \times O P = \hat{i} 12 \hat{j} 10 \hat{k} 12 = \hat{i} (2 - 0) - \hat{j} (2 - 2) + \hat{k} (0 - 2) = 2 \hat{i} - 2 \hat{k}$ .
½ mark
Area $= 4 + 4 = 22$ square units.
½ mark

Answer: $22$ sq. units

Where the marks are

Finds $O P = 2 \hat{i} + 2 \hat{k}$ (½ mark)
Uses area $= ∣ O A \times O P ∣$ (½ mark)
Computes cross product $2 \hat{i} - 2 \hat{k}$ (½ mark)
Area $22$ sq. units (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 paperSample paper 2025-26: every question, by section.

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CBSE Class 12 Mathematics sample paper 2025-26: question 25

Hints

Step-by-step solution

Revise the chapter

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