Search any question & find its solution
Question:
Answered & Verified by Expert
If $\overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}, \overrightarrow{\mathrm{b}}=3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=5 \hat{\mathrm{i}}+4 \hat{\mathrm{k}}$ are three vectors, then a vector which is perpendicular to $\vec{a}$ and $\vec{b} \times \vec{c}$ is
Options:
Solution:
2609 Upvotes
Verified Answer
The correct answer is:
$-45 \hat{i}+30 \hat{j}+4 \hat{k}$
Vector perpendicular to $\vec{a}$ and $(\vec{b} \times \vec{c})$ will be
$$
\begin{aligned}
& \vec{a} \times(\vec{b}+\vec{c})=(\vec{a} \cdot \vec{c}) \vec{b}-(\vec{a} \cdot \vec{b}) \vec{c} \\
& =(10)(3 \hat{j}+4 \hat{k})-(9)(5 \hat{i}+4 \hat{k}) \\
& =(-45 \hat{i}+30 \hat{j}+4 \hat{k})
\end{aligned}
$$
$$
\begin{aligned}
& \vec{a} \times(\vec{b}+\vec{c})=(\vec{a} \cdot \vec{c}) \vec{b}-(\vec{a} \cdot \vec{b}) \vec{c} \\
& =(10)(3 \hat{j}+4 \hat{k})-(9)(5 \hat{i}+4 \hat{k}) \\
& =(-45 \hat{i}+30 \hat{j}+4 \hat{k})
\end{aligned}
$$
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.