Question

If the vectors$-\widehat{3i}=\widehat{4j}-\widehat{2k}$, $\hat{i}+\widehat{2k}$, $\hat{i}-\widehat{pj}$ are coplanar then the value of p is ?

Answer 1

Given that the vector $-3\hat{i}+4\hat{j}-2\hat{k},\hat{i}+2\hat{k},\hat{i}-p\hat{j}$ are coplaner

so

$\left[-3\hat{i}+4\hat{j}-2\hat{k},\hat{i}+2\hat{k},\hat{i}-p\hat{j}\right]=0$

$\left(-3\hat{i}+4\hat{j}-2\hat{k}\right)\cdot \left|\begin{array}{c}\hat{i}\hat{j}\hat{k}\\ 102\\ 1-p0\end{array}\right|=0$

$\left(-3\hat{i}+4\hat{j}-2\hat{k}\right)\cdot \left(2p\hat{i}+2\hat{j}-2p\right)=0$

$-6p+8+2p=0$

$8=4p$

$p=2$