Question

If $\overline{a},\overline{b},\overline{c}$ are non collinear, non coplanar vectors and $x\overline{a}+\overline{b},x\overline{b}+\overline{c},x\overline{c}+\overline{a}$ are coplanar vectors then the value of x is

• A. 1
• B. 0
• C. -1
• D. any real number

Answer 1

The correct option is C

-1

$\left[\overline{a}\overline{b}\overline{c}\right]\ne 0$

$\left|\begin{array}{ccc}x& 1& 0\\ 0& x& 1\\ 1& 0& x\end{array}\right|=0\Rightarrow x^3+1=0\Rightarrow x=-1$