Let P be the plane 3 x + 2y + 3z = 16 and let S = i + j + k : ^2 + ^2 + ^2 = 1 and the distance of ( , , )...

Question

Let P be the plane 3 x + 2y + 3z = 16 and let S = i + j + k : ^2 + ^2 + ^2 = 1 and the distance of ( , , ) 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 , v and w . Then the value of 80 3 V is _____.

Accepted Answer

45

JEE Advanced 2023 Mathematics question

Solution

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