1 2 3 4 5 For what values of b are the given vectors orthogo

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For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated list.) (- 22, b, 6), b, b2, b b=

Solution

1. For two vectors to be orthogonal, a.b = 0 ( a is a vector, b is a vector)

a= (-22i + bj 6k)

b = (b i + b² j + b k)

a.b = (-22i + bj + 6k). (b i+ b² j + b k)

0 = -22b + b³ + 6b

b³ - 16b = 0

b(b² - 16) = 0

b = 0 or b² = 16

b = 0 or b= 4 or b = -4

b = 0,4,-4