For what values of b are the given vectors orthogonal Enter

For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated list.) <39, b, 3> , < b, b², b>

b = ?

Solution

Answer :

Let us denote the vectors by U = < - 39 , b , 3 > and V = < b , b² , b >

Then if U and V are orthogonal , it is true that U.V = 0

That is < - 39 , b , 3 > . < b , b² , b > = 0

             - 39b + b³ + 3b = 0

              b³ - 36b = 0

              b( b² - 36) = 0

              b = 0 or b² = 36

Therefore, the values of b for which the given vectors are orthogonal are b = 0 , - 6 , 6