How do you find the inner product and state whether the vectors are perpendicular given #<4,9,-3>*<-6, 7,5>#?

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Answer 1 · 2016-10-16T23:09:01

#< 4,9,-3 > * < -6,7,5 > =24#

They are not perpendicular.

In #RR^3#, the inner product, or dot product, is given by

#< x_1, y_1, z_1 > * < x_2, y_2, z_2 > = x_1x_2+y_1y_2+z_1z_2#

Two vectors are perpendicular if and only if their inner product is #0#.

In the case of our given vectors, then, we have

#< 4,9,-3 > * < -6,7,5 > = 4(-6)+9(7)+(-3)(5)#

#=-24+63-15#

#=24#

As the inner product of the two vectors is not #0#, they are not perpendicular.