CBSE Class 12 Mathematics 2023: question 22

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. $|\hat{i}+\hat{j}+\hat{k}|=\sqrt{3}$, so the unit vector along it is $\frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}+\frac{1}{\sqrt{3}}\hat{k}$.

   1 mark

2. A collinear vector of magnitude $3\sqrt{3}$ is $\pm 3\sqrt{3}\times$ (unit vector). Taking the $+$ sign gives $3\hat{i}+3\hat{j}+3\hat{k}$.

   ½ mark

3. Taking the $-$ sign gives $-3\hat{i}-3\hat{j}-3\hat{k}$.

   ½ mark

Answer: $3\hat{i}+3\hat{j}+3\hat{k}$ and $-3\hat{i}-3\hat{j}-3\hat{k}$

Revise the chapter

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