How do you find the inner product and state whether the vectors are perpendicular given #<4,5,1>*<-1,-2,3>#?

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Answer 1 · 2017-01-14T08:48:09

#-11#, and not perpendicular

The inner product ( or scalar dot product) of wo vectors

#veca=((a_1),(a_2),(a_3))#

#vecb=((b_1),(b_2),(b_3))#

is defined as:

#veca.vecb=|veca||vecb|costheta" " #where #theta# is the angle bewteen the vectors.

and can be calculated using the result

#veca.vecb=a_1b_1+a_2b_2+a_3b_3#

so for the vectors in this question we have;

#veca=((4),(5),(1))#

#vecb=((-1),(-2),(3))#

#veca.vecb=((4),(5),(1)).((-1),(-2),(3))#

#veca.vecb=4xx(-1)+5xx(-2)+1xx3#

#veca.vecb=-4-10+3=-11#

for the vectors to be perpendicular ie. #theta=90^0," "costheta=0#

#=>veca.vecb=0#

in this case #veca.vecb!=0, :." "#not perpendicular