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If $\mathbf{p}=\hat{i}+\hat{j}, \mathbf{q}=4 \hat{k}-\hat{j}$ and $\mathbf{r}=\hat{i}+\hat{k}$, then the unit vector in the direction of $3 \mathbf{p}+\mathbf{q}-2 \mathbf{r}$ is
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Verified Answer
The correct answer is:
$\frac{1}{3}(\hat{i}+2 \hat{j}+2 \hat{k})$
$3 p+q-2 \mathbf{r}$
$$
\begin{aligned}
& =3(\hat{i}+\hat{j})+(4 \hat{k}-\hat{j})-2(\hat{i}+\hat{k}) \\
& =\hat{i}+2 \hat{j}+2 \hat{k}
\end{aligned}
$$
$\therefore$ Unit vector in the direction of
$$
3 \mathbf{p}+\mathbf{q}-2 \mathbf{r}=\frac{1}{3}(\hat{i}+2 \hat{j}+2 \hat{k})
$$
$$
\begin{aligned}
& =3(\hat{i}+\hat{j})+(4 \hat{k}-\hat{j})-2(\hat{i}+\hat{k}) \\
& =\hat{i}+2 \hat{j}+2 \hat{k}
\end{aligned}
$$
$\therefore$ Unit vector in the direction of
$$
3 \mathbf{p}+\mathbf{q}-2 \mathbf{r}=\frac{1}{3}(\hat{i}+2 \hat{j}+2 \hat{k})
$$
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