The projection of on is:
The projection of $\hat{\imath} + 2\hat{\jmath} - 3\hat{k}$ on $2\hat{\imath} - \hat{\jmath} + \hat{k}$ is:
- a$\frac{\sqrt{3}}{\sqrt{2}}$
- b$-\frac{\sqrt{3}}{\sqrt{2}}$
- c$\frac{-3}{2}$
- d$\frac{-\sqrt{3}}{2}$
Answer
Answer
AIWritten by AI (gemini-2.5-pro) - it can contain mistakes.
Correct option: b
Answer: (b) $-\frac{\sqrt{3}}{\sqrt{2}}$
The projection of $\vec{a} = \hat{\imath} + 2\hat{\jmath} - 3\hat{k}$ on $\vec{b} = 2\hat{\imath} - \hat{\jmath} + \hat{k}$ is $\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|} = \frac{1(2) + 2(-1) + (-3)(1)}{\sqrt{2^2 + (-1)^2 + 1^2}} = \frac{2 - 2 - 3}{\sqrt{6}} = -\frac{3}{\sqrt{6}} = -\frac{\sqrt{3}}{\sqrt{2}}$.
From ISC 2026 Mathematics Paper 1, question 15(ii).