If the four points with position vectors $-2\hat i+\hat j + \hat k, \hat i+\hat j+\hat k,\hat j- \hat k$ and $\lambda \hat j + \hat k$ are coplanar, then $\lambda$ is equal to

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Aicharya · Accepted Answer

If four points $\left(x_{1}, y_{1}, z_{1}ight),\left(x_{2}, y_{2}, z_{2}ight),\left(x_{3}, y_{3}, z_{3}ight)$ and $\left(x_{4}, y_{4}, z_{4}ight)$ are coplanar, then $\left|\begin{array}{lll}x_{2}-x_{1} & y_{2}-y_{1} & z_{2}-z_{1} \ x_{3}-x_{1} & y_{3}-y_{1} & z_{3}-z_{1} \ x_{4}-x_{1} & y_{4}-y_{1} & z_{4}-z_{1}\end{array}ight|=0$ Now, $\quad\left|\begin{array}{ccc}3 & 0 & 0 \ 2 & 0 & -2 \ 2 & \lambda-1 & 0\end{array}ight|=0$ $\Rightarrow \quad 3(0+2 \lambda-2)=0$ $\lambda=1$

If the four points with position vectors $-2\hat i+\hat j + \hat k, \hat i+\hat j+\hat k,\hat j- \hat k$ and…

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