Question

If the points with position vectors $10\hat{i}+3\hat{j},12\hat{i}-5\hat{j}$ and $x\hat{i}+11\hat{j}$ are collinear, then $x$ =

• A. - 8
• B. 4
• C. 8
• D. - 4

Answer 1

Answer: (C)

The vectors $10\hat{i}+3\hat{j},12\hat{i}-5\hat{j}$ and $x\hat{i}+11\hat{j}$ are collinear.
$\therefore \Delta =\left|\begin{array}{ccc}10& 3& 1\\ 12& -5& 1\\ x& 11& 1\end{array}\right|=0$
$\Rightarrow 10\left(-5-11\right)-3\left(12-x\right)+1\left(132+5x\right)=0$
$\Rightarrow -160-36+3x+132+5x=0$
$\Rightarrow 8x-+4=0\Rightarrow x=8$