Q41 / 60 · IAT (IISER) 2022 · Mathematics
Consider the vectors
$\begin{aligned} \vec{a} & =\hat{i}+x \hat{j}+2 \hat{k} \\ \vec{b} & =\hat{i}+2 \hat{j}+x \hat{k} \\ \vec{c} & =2 \hat{i}+\hat{j}+3 \hat{k}\end{aligned}$
The values of $x$ for which there is at least one nonzero vector perpendicular to the vectors $\vec{a}, \vec{b}$ and $\vec{c}$ are
$\begin{aligned} \vec{a} & =\hat{i}+x \hat{j}+2 \hat{k} \\ \vec{b} & =\hat{i}+2 \hat{j}+x \hat{k} \\ \vec{c} & =2 \hat{i}+\hat{j}+3 \hat{k}\end{aligned}$
The values of $x$ for which there is at least one nonzero vector perpendicular to the vectors $\vec{a}, \vec{b}$ and $\vec{c}$ are
- A$7 / 2,0$
- Correct answerB0,2
- C$-2,2$
- D$4,-2$
Hence, the correct answer is option: 'B'.