Question

If the four points, whose position vectors are $3 \hat{i}-4 \hat{j}+2 \hat{k}, \hat{i}+2 \hat{j}-\hat{k},-2 \hat{i}-\hat{j}+3 \hat{k} $ and $5 \hat{ i }-2 \alpha \hat{ j }+4 \hat{ k }$ are coplanar, then $\alpha$ is equal to

• A. $\frac{107}{17}$
• B. $\frac{73}{17}$
• C. $-\frac{73}{17}$
• D. $-\frac{107}{17}$

Answer 1

Answer: (B)

Let $A :(3,-4,2) C :(-2,-1,3)$
$\text { B : }(1,2,-1) \text { D : }(5,-2 \alpha, 4)$
$A, B, C, D $ are coplanar points, then
$ \Rightarrow\begin{vmatrix} 1-3 & 2+4 & -1-2 \\-2-3 & -1+4 & 3-2 \\5-3 & -2 \alpha+4 & 4-2\end{vmatrix}=0 $
$ \Rightarrow \alpha=\frac{73}{17}$