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

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