Search any question & find its solution
Question:
Answered & Verified by Expert
If $\mathbf{a}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-5 \mathbf{k}$, $\mathbf{c}=3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-\hat{\mathbf{k}}$, then a vector perpendicular to $\mathbf{a}$ and in the plane containing $\mathbf{b}$ and $\mathbf{c}$ is
Options:
Solution:
1143 Upvotes
Verified Answer
The correct answer is:
$-17 \hat{\mathbf{i}}-21 \hat{\mathbf{j}}-97 \hat{\mathbf{k}}$
We know that a vector perpendicular to $\mathbf{a}$ and in the plane containing $\mathbf{b}$ and $\mathbf{c}$ is given by
$\therefore \quad \mathbf{b} \times \mathbf{c}=\left|\begin{array}{ccc}\hat{\mathbf{i}} & \hat{\mathbf{j}} & \hat{\mathbf{k}} \\ 1 & 2 & -5 \\ 3 & 5 & -1\end{array}\right|$
Now, $\mathbf{a} \times(\mathbf{b} \times \mathbf{c})=\left|\begin{array}{ccc}\hat{\mathbf{i}} & \hat{\mathbf{j}} & \hat{\mathbf{k}} \\ 2 & 3 & -1 \\ 23 & -14 & -1\end{array}\right|$
which is the required vector.
$\therefore \quad \mathbf{b} \times \mathbf{c}=\left|\begin{array}{ccc}\hat{\mathbf{i}} & \hat{\mathbf{j}} & \hat{\mathbf{k}} \\ 1 & 2 & -5 \\ 3 & 5 & -1\end{array}\right|$
Now, $\mathbf{a} \times(\mathbf{b} \times \mathbf{c})=\left|\begin{array}{ccc}\hat{\mathbf{i}} & \hat{\mathbf{j}} & \hat{\mathbf{k}} \\ 2 & 3 & -1 \\ 23 & -14 & -1\end{array}\right|$
which is the required vector.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.