Question

If $(k,1,-2),(1,1,3)(8,5,0)$ are coplaner vectors, then k$=$ _____________.

• A. $-2$
• B. $-5$
• C. $2$
• D. $5$

Answer 1

Answer: (C)

$2$

Here given vectors are coplanar
$\therefore \left|\begin{array}{ccc}k& 1& -2\\ 1& 1& 3\\ 8& 5& 0\end{array}\right|=0$
$\therefore k(0-15)-1(0-24)-2(5-8)=0$
$\therefore -15k-1(-24)-2(-3)=0$
$\therefore -15k+24+6=0$
$\therefore -15k=-30$
$\therefore k=2$.