Question

The value of P so that the vectors $2i-j+k,$ $i+2j-3k$ and $3i+pj+5k$ are coplanar should be

• A. 16
• B. $-4$
• C. 4
• D. $-8$

Answer 1

Answer: (B)

For coplanarity $\left|\begin{array}{ccc}2& -1& 1\\ 1& 2& -3\\ 2& P& 5\end{array}\right|=0$ $2(10+3P)+1(5+9)+1(P-6)=0$ $20+6P+5+9+P-6=0$ $7P+34-6=0$ $7P+28=0$ $7P=-28$ $P=-\frac{28}{7}=-4$