CBSE Class 12 Mathematics 2026: question 24

Hints

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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.

1. One diagonal: $\vec{a}+\vec{b}=(3+1)\hat{i}+(-2+0)\hat{j}+(2+2)\hat{k}=4\hat{i}-2\hat{j}+4\hat{k}$ (or its negative)

   ½ mark

2. Other diagonal: $\vec{a}-\vec{b}=2\hat{i}-2\hat{j}+0\hat{k}=2\hat{i}-2\hat{j}$ (or its negative)

   ½ mark

3. Lengths: $|\vec{a}+\vec{b}|=\sqrt{16+4+16}=6$ and $|\vec{a}-\vec{b}|=\sqrt{4+4}=2\sqrt{2}$

   1 mark

Answer: Diagonals $4\hat{i}-2\hat{j}+4\hat{k}$ and $2\hat{i}-2\hat{j}$; lengths 6 and $2\sqrt{2}$

Revise the chapter

• Chapter: Vector Algebra (notes, formulas, where marks are lost and every past question)