Let P be the plane 3 x + 2 y + 3 z = 16 and let S = α i ^ + β j ^ + γ k ^ : α 2 + β 2 + γ 2 = 1 and the distance of α , β , γ from the plane P is 7 2 . Let u → , v → and w → be three distinct vectors in S such that u → - v → = v → - w → = w → - u → . Let V be the volume of the parallelepiped determined by vectors u &#85

Step-by-step solution

Given, Equation of plane, P : 3 x + 2 y + 3 z = 16 And S = α i ^ + β j ^ + γ k ^   :   α 2 + β 2 + γ 2 = 1 which is equation of sphere, Also distance, d α ,   β ,   γ from P = 7 2 And relation between distinct vector is given by, u → - v → = v → - w → = w → - u → Now V : volume of parallelepiped by vectors u → ,   v → ,   w → So, using formula of distance d α ,   β ,