The projection of îm̂ât̂ĥ + 2ĵm̂ât̂ĥ - 3k̂ on 2îm̂ât̂ĥ - ĵm̂ât̂ĥ + k̂ 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$\frac{-\sqrt{3}}{2}$

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Answer

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 $\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|} = \frac{1(2) + 2(-1) + (-3)(1)}{\sqrt{2^2 + (-1)^2 + 1^2}} = \frac{2 - 2 - 3}{\sqrt{6}} = -\frac{3}{\sqrt{6}} = -\frac{\sqrt{3}}{\sqrt{2}}$.