Question

For which value of $a$ the vector $a\hat{i},3\hat{i}+a\hat{j}+4\hat{k}$ and $\hat{i}+\hat{j}+a\hat{k}$ are non coplanar.

• A. $2,-2$
• B. $0$
• C. $1,-1$
• D. $3,-3$

Answer 1

The correct option is C $1,-1$

For the vectors $ai,3i+aj+4k,i+j+ak$ to be non co planar

$\left|\begin{array}{ccc}a& 0& 0\\ 3& a& 4\\ 1& 1& a\end{array}\right|\ne 0$

$a(a^2-4)\ne 0$

$a\ne 0,2,-2$

$\therefore a$ is non co planar for $a=1,-1$