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Question: Answered & Verified by Expert
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:
MathematicsVector AlgebraAP EAMCETAP EAMCET 2005
Options:
  • A $\pm(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}})$
  • B $\pm 3(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}})$
  • C $(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})$
  • D $\pm 21(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}})$
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 .

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