Question

If the points $(5,4,2),(8,k,-7)$ and $(6,2,-1)$ are collinear, then $k=$

• A. $-2$
• B. $2$
• C. $10$
• D. $1$

Answer 1

The correct option is A $-2$

For collinear points in $3-$Dimensional.

Their determinant should be zero.

$\left|\begin{array}{ccc}5& 4& 2\\ 8& k& -7\\ 6& 2& -1\end{array}\right|=0$

$⟹5(-k+14)-4(-8+42)+2(16-6K)=0$

$⟹-17k-34=0$

$⟹k=-2$