How do you find the inner product and state whether the vectors are perpendicular given #<3,4,0>*<4,-3,6>#?

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Answer 1 · 2017-02-11T07:14:44

The inner product is #=0#

The dot product or inner product of 2 vectors #veca# and #vecb# is

#veca.vecb=〈a_1,a_2,a_3〉.〈b_1,b_2,b_3〉=a_1b_1+a_2b_2+a_3b_3#

Here,

#veca=<3,4,0>#

#vecb=<4,-3,6>#

The inner product is

#<3,4,0>.<4,3,-6> =3*4-4*3+0=12-12=0#

As the inner product is #=0#, the 2 vectors are perpendicular