The parallelopiped is determined by vectors a = -2 i + 5 j + 3 k , b = i + 3 j - 2 k , c = -3 i + j + 4 k . The altitude of parallelopiped on the parallelogram base determined by vectors b and c is

Step-by-step solution

The volume of the parallelepiped is given by the scalar triple product V = |[ a b c ]| . V = | matrix -2 & 5 & 3 1 & 3 & -2 -3 & 1 & 4 matrix | V = |-2(12 + 2) - 5(4 - 6) + 3(1 + 9)| V = |-28 + 10 + 30| = 12 The area of the parallelogram base determined by vectors b and c is A = | b c | . b c = | matrix i & j & k 1 & 3 & -2 -3 & 1 & 4 matrix | b c = i (12 + 2) - j (4 - 6) + k (1 + 9) = 14 i + 2 j + 10 k A = 14^2 + 2^2 + 10^2 = 196 + 4 + 100 = 300 = 10 3 The altitude h of the parallelepiped is the volume divided by