Practicing Success
Practicing Success
CUET Preparation Today
| The value of scalar \(p\) such that vectors \(2\hat{i}-\hat{j}+\hat{k},\hat{i}+2\hat{j}-3\hat{k}\) and \(3\hat{i}+p\hat{j}+5\hat{k}\) are coplanar is |
\(3\) \(-3\) \(-4\) \(4\) |
| \(-4\) |
| Given, \(\vec{a}=2\hat{i}-\hat{j}+\hat{k},\vec{b}=\hat{i}+2\hat{j}-3\hat{k},\vec{c}=3\hat{i}+p\hat{j}+5\hat{k}\hspace{9cm}\) If \(\vec{a},\vec{b},\vec{c}\) are coplanar \(\vec{a}\cdot (\vec{b}\times \vec{c})=0\hspace{6cm}\) \(\begin{aligned}\left|\begin{array}{lll}2&-1&1\\ 1& 2&-3\\ 3& p& 5\end{array}\right|&=0\\ 2(10+3p)+1(5+9)+1(p-6)&=0\\ 20+6p+14+p-6 &=0\\ 7p+28&=0\\ p&=-4\end{aligned}\) |
