The altitude of the parallelopiped, whose coterminus edges are the vectors a = i + j + k , b =2 i +4 j - k , c = i + j +3 k , where a , ~b are the sides of the base of parallelopiped, is

Step-by-step solution

Given the coterminous edges of the parallelepiped: a = i + j + k b = 2 i +4 j - k c = i + j +3 k The volume is the absolute value of the scalar triple product: V = |( a b ) c | = | vmatrix 1 & 1 & 1 2 & 4 & -1 1 & 1 & 3 vmatrix | = |1(12+1) - 1(6+1) + 1(2-4)| = |13 - 7 - 2| = 4 The base area is the magnitude of the cross product a b : a b = vmatrix i & j & k 1 & 1 & 1 2 & 4 & -1 vmatrix = -5 i + 3 j + 2 k | a b | = (-5)^2 + 3^2 + 2^2 = 38 The altitude is given by h = V | a b | = 4 38 Final altitude: 4 38