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If the vector $\mathbf{a}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$ and $\mathbf{b}$ are collinear and $|\mathbf{b}|=21$, then $\mathbf{b}$ equal to:
Options:
Solution:
1119 Upvotes
Verified Answer
The correct answer is:
$\pm 3(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}})$
Given that $\mathbf{a}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$
and
$|\mathbf{b}|=21$
Now, taking option (b)
Let
$\begin{aligned}
\mathbf{b} & = \pm 3(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}) \\
|\mathbf{b}| & =3 \sqrt{4+9+36}=21 \\
\mathbf{b} & = \pm 3 \mathbf{a}
\end{aligned}$
and
$\therefore \mathbf{a}$ and $\mathbf{b}$ are collinear and magnitude of $\mathbf{b}$ is 21 .
and
$|\mathbf{b}|=21$
Now, taking option (b)
Let
$\begin{aligned}
\mathbf{b} & = \pm 3(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}) \\
|\mathbf{b}| & =3 \sqrt{4+9+36}=21 \\
\mathbf{b} & = \pm 3 \mathbf{a}
\end{aligned}$
and
$\therefore \mathbf{a}$ and $\mathbf{b}$ are collinear and magnitude of $\mathbf{b}$ is 21 .
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