Find all values of b for which the vectors 5, −4, 4 and b2, b, 0 are orthogonal. (Enter your answers as a commaseparated list.)
Mathematics
megantdev
Question
Find all values of
b
for which the vectors
5, −4, 4
and
b2, b, 0
are orthogonal. (Enter your answers as a commaseparated list.)
b
for which the vectors
5, −4, 4
and
b2, b, 0
are orthogonal. (Enter your answers as a commaseparated list.)
1 Answer

1. User Answers LammettHash
The vectors will be orthogonal if their dot product is zero.
[tex]\langle5,4,4\rangle\cdot\left\langle b^2,b,0\right\rangle=5b^24b=0[/tex]
You have
[tex]5b^24b=b(5b4)=0\implies b=0,b=\dfrac45[/tex]