If $\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+\hat{j}-2 \hat{k}$ and $\bar{c}=4 \hat{i}-2 \hat{j}+\hat{k}$, then the unit vector in the direction of $3 \bar{a}+\bar{b}-2 \bar{c}$ is

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Aicharya · Accepted Answer

$\begin{aligned} & 3 \overline{\mathrm{a}}+\overline{\mathrm{b}}-2 \overline{\mathrm{c}} \ & =3(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})+(\hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}})-2(4 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}) \ & =-(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}} \end{aligned}$ $	herefore \quad$ The unit vector in the direction of $3 \overline{\mathrm{a}}+\overline{\mathrm{b}}-2 \overline{\mathrm{c}}$ is $\begin{aligned} & \frac{-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}}}{|\hat{-\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}}|} \ & =\frac{-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{(-1)^2+2^2+(-1)^2}} \ & =\frac{1}{\sqrt{6}}(-\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}}) \end{aligned}$

If $\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+\hat{j}-2 \hat{k}$ and $\bar{c}=4 \hat{i}-2…

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