Let $\mathbf{u}=-2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{v}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$. Then the component of $\mathbf{v}$ on $\mathbf{u}$ is

Question

Let $\mathbf{u}=-2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{v}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$. Then the component of $\mathbf{v}$ on $\mathbf{u}$ is, $\frac{4}{3}$, $\frac{-4}{3}$, $\frac{-2}{3}$, $\frac{2}{3}$

MARKS App · Accepted Answer

Given vectors are $\mathbf{u}=-2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{v}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ $\therefore$ Component of $\mathbf{v}$ on $\mathbf{u}$ is $=\frac{\mathbf{v} \cdot \mathbf{u}}{|\mathbf{u}|}=\frac{-2-4+2}{\sqrt{4+4+1}}=\frac{-4}{3}$ Hence, option (b) is correct.

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