BITSAT 2012 Paper

We know that the length of the perpendicular from the point ($x_1, y_1, z_1$) to the plane ax + by + cz + d = 0 is $\frac{\left| ax_1+by_1+cz_1+d \right|}{\sqrt{a^2+b^2+c^2}}$ and the co-ordinate (α, β, γ) of the foot of the ⊥ are given by $\frac{\alpha - x_1}{a}$ = $\frac{\beta - y_1}{b}$ = $\frac{\gamma - z_1}{c}$ = - $\left(\frac{ax_1+by_1+cz_1+d}{a^2+b^2+c^2}\right)$ ... (1) In the given ques, $x_1$ = 7, $y_1$ = 14, $z_1$ = 5, a = 2 b = 4,c = -1, d = -2 By putting these values in (1), we get $\alpha7\cdot2$ = $\frac{\beta-14}{4}$ = $\frac{\gamma-5}{-1}$ = - $\frac{63}{21}$ ⇒ α = 1 , β = 2 and γ = 8