The square of the distance of the image of the point $(6,1,5)$ in the line $\frac{x-1}{3}=\frac{y}{2}=\frac{z-2}{4}$, from the origin is _________

Question

Aicharya · Accepted Answer

Let $\mathrm{M}(3 \lambda+1,2 \lambda, 4 \lambda+2)$ $\overrightarrow{\mathrm{AM}} \cdot \overrightarrow{\mathrm{b}}=0$ $\Rightarrow \quad 9 \lambda-15+4 \lambda-2+16 \lambda-12=0$ $\Rightarrow \quad 29 \lambda=29$ $\Rightarrow \quad \lambda=1$ $\mathrm{M}(4,2,6), \mathrm{I}=(2,3,7)$ Required Distance $=\sqrt{4+9+49}=\sqrt{62}$ Ans. 62

The square of the distance of the image of the point $(6,1,5)$ in the line…

Solution