Question

The equation of the straight line passing through the origin and perpendicular to the lines $\frac{x+1}{-3}=\frac{y-2}{2}=\frac{z}{1}$ and $\frac{x-1}{1}=\frac{y}{-3}=\frac{z+1}{2}$ has the equation.

• A. $x=y=z$
• B. $\frac{x}{4}=\frac{y}{3}=\frac{z}{6}$
• C. $\frac{x}{3}=\frac{y}{1}=\frac{z}{0}$
• D. none of these

Answer 1

The correct option is A $x=y=z$

Direction ratio of lines are $(-3,2,1)$ and $(1,-3,2)$ respectively. So direction ratio of the required line will be cross product of these because required line is perpendicular to the both given lines
$\left|\begin{array}{ccc}i& j& k\\ -3& 2& 1\\ 1& -3& 2\end{array}\right|$
On expanding we get;
$7\hat{i}+7\hat{j}+7\hat{k}$
Therefore, Direction ratio of line is $(1,1,1)$ and it passes through $(0,0,0)$
Hence, the equation of the line will be $x=y=z$