Question

The point in which the line joining of A(– 9, 4, 5) and B(11, 0, –1) is met by the perpendicular drawn from the origin is

• A. (2, 2, 1)
• B. (2, 1, 2)
• C. (1, 2, 2)
• D. (2, 2, 2)

Answer 1

The correct option is C (1, 2, 2)

Let P be the required point on AB. Let P divides AB in the ratio $\lambda :1$
​$P=(\frac{11\lambda -9}{\lambda +1},\frac{4}{\lambda +1},\frac{5-\lambda }{\lambda +1}),OP\perp AB\Rightarrow 20\left(\frac{11\lambda -9}{\lambda +1}\right)-4\left(\frac{4}{\lambda +1}\right)-6\left(\frac{5-\lambda }{\lambda +1}\right)=0\therefore \lambda =1\Rightarrow P=(1,2,2)$