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megantdev megantdev
  • 31-01-2017
  • Mathematics
Answered

Find all values of

b

for which the vectors


5, −4, 4


and


b2, b, 0


are orthogonal. (Enter your answers as a comma-separated list.)

Verified Answer :

LammettHash
LammettHash LammettHash
  • 01-02-2017

The vectors will be orthogonal if their dot product is zero.

\(\langle5,-4,4\rangle\cdot\left\langle b^2,b,0\right\rangle=5b^2-4b=0\)

You have

\(5b^2-4b=b(5b-4)=0\implies b=0,b=\dfrac45\)

Answer Link

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