If A, B and C be three non-collinear points such that AB = i + 2j - k and AC = 2i - 3j, then find the area of Δ ABC.

MathsCBSE Class 12 · Board exam 2026, set 65/5/1 · 2 marks · Very short answer

CBSE Class 12 Mathematics 2026: question 24(b)

Set in the CBSE Class 12 board exam of 2026, 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

If A, B and C be three non-collinear points such that $A B = \hat{i} + 2 \hat{j} - \hat{k}$ and $A C = 2 \hat{i} - 3 \hat{j}$ , then find the area of $Δ$ ABC.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 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 triangle is half the magnitude of the cross product of two side vectors.

Hint 2

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

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.

Area of $Δ A B C = \frac{1}{2} ∣ A B \times A C ∣$ .
$A B \times A C = \hat{i} 12 \hat{j} 2 - 3 \hat{k} - 1 0 = \hat{i} (0 - 3) - \hat{j} (0 + 2) + \hat{k} (- 3 - 4) = - 3 \hat{i} - 2 \hat{j} - 7 \hat{k}$
1 mark
$∣ A B \times A C ∣ = 9 + 4 + 49 = 62$ , so the area is $\frac{62}{2}$ sq. units.
1 mark

Answer: $\frac{62}{2}$ sq. units

Where the marks are

Uses the area formula and finds $A B \times A C = - 3 \hat{i} - 2 \hat{j} - 7 \hat{k}$ (1 mark)
Area $= \frac{62}{2}$ sq. units (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 paper2026 board paper, set 65/5/1: every question, by section.

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CBSE Class 12 Mathematics 2026: question 24(b)

Hints

Step-by-step solution

Revise the chapter

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