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Q.
If vectors $2 \hat{ i }-\hat{ j }+\hat{ k }, \hat{ i }+2 \hat{ j }-3 \hat{ k }$ and $3 \hat{ i }+a \hat{ j }+5 \hat{ k }$ are coplanar, then find value of ' $a$ '.
Vector Algebra
Solution:
$\begin{vmatrix}2 & -1 & 1 \\ 1 & 2 & -3 \\ 3 & a & 5\end{vmatrix}=0$
$\Rightarrow 3(3-2)+ a (1+6)+5(4+1)=0$
$\Rightarrow 3+7 a +25=0 $
$\Rightarrow a =-\frac{28}{7}$