Question

Let P be the plane √3x+2y+3z =16 and let and let S = {$\alpha \hat{i}+\beta \hat{j}+\gamma\hat{k}:\alpha^2+\beta^2+\gamma^2=1$ and the distance of (α, β, γ) from the plane P is $\frac{7}{2}$ }. Let u, v, and w be three distinct vectors in s such that |$\vec{u}-\vec{v}$| = |$\vec{v}-\vec{w}$| = |$\vec{w}-\vec{u}$|. Let V be the volume of the parallelepiped determined by vectors $\vec{u},\vec{v},\vec{w}$. Then the value of $\frac{80}{\sqrt3}$V is

Answer 1

The correct answer will be 45