Question:
Let $a, b$ and $c$ be distinct positive numbers. If the vectors $a \hat{i}+a \hat{j}+c \hat{k}, \hat{i}+\hat{k}$ and $c \hat{i}+c \hat{j}+b \hat{k}$ are co-planar, then $\mathrm{c}$ is equal to:
Correct Option: , 4
Solution:
Because vectors are coplanar
Hence $\left|\begin{array}{lll}\mathrm{a} & \mathrm{a} & \mathrm{c} \\ 1 & 0 & 1 \\ \mathrm{c} & \mathrm{c} & \mathrm{b}\end{array}\right|=0$
$\Rightarrow \mathrm{c}^{2}=\mathrm{ab} \Rightarrow \mathrm{c}=\sqrt{\mathrm{ab}}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.