MathsCBSE Class 12 · Board exam 2023, set 65/5/1 · 2 marks · Very short answer

CBSE Class 12 Mathematics 2023: question 24(b)

Set in the CBSE Class 12 board exam of 2023, paper 65/5/1, section B, question 24(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(b) · 2 marks · Very short answerVector Algebra

Find the area of a parallelogram whose adjacent sides are determined by the vectors $a = \hat{i} - \hat{j} + 3 \hat{k}$ and $b = 2 \hat{i} - 7 \hat{j} + \hat{k}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 65/5/1.

Hints

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

Hint 1

The area of a parallelogram with adjacent sides $a, b$ is $∣ a \times b ∣$ .

Hint 2

Expand the 3×3 determinant with $\hat{i}, \hat{j}, \hat{k}$ in the first row, then find its magnitude.

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.

$a \times b = \hat{i} 12 \hat{j} - 1 - 7 \hat{k} 31$
$= \hat{i} (- 1 + 21) - \hat{j} (1 - 6) + \hat{k} (- 7 + 2)$
$= 20 \hat{i} + 5 \hat{j} - 5 \hat{k}$
1½ marks
Area of parallelogram $= ∣ a \times b ∣ = 400 + 25 + 25 = 450 = 152$ sq units
½ mark

Answer: $152$ sq units

Where the marks are

Correct cross product $20 \hat{i} + 5 \hat{j} - 5 \hat{k}$ (1½ marks)
Area $= ∣ a \times b ∣ = 152$ 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 paper2023 board paper, set 65/5/1: every question, by section.

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CBSE Class 12 Mathematics 2023: question 24(b)

Hints

Step-by-step solution

Revise the chapter

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