Discussion Forum

1)

If the vectors   $a=\hat{i}+\hat{j}+\hat{k}$. $b=\hat{i}-\hat{j}+2\hat{k}$ and $c=x\hat{i}+(x-2)\hat{j}-\hat{k}$

are coplanar , then x=

Answer:

Option D

Explanation:

Given, 

$a=\hat{i}+\hat{j}+\hat{k}$.

$b=\hat{i}-\hat{j}+2\hat{k}$

and $c=x\hat{i}+(x-2)\hat{j}-\hat{k}$

 Since  , the given vectors are coplanar  , therefore

   [a  b  c]=0

  $\Rightarrow$    $\begin{bmatrix}1 & 1&1 \\1 & -1&2\\x&x-2&-1 \end{bmatrix}=0$

 $\Rightarrow$   $1(1-2x+4)-1(-1-2x)+1(x-2+x)=0$

 $\Rightarrow$   $5-2x+1+2x+2x-2=0$

 $\Rightarrow$   $2x+4=0$

 $\Rightarrow$    $2x=-4$

 $\Rightarrow$     $x=-2$