If A=<3,1,−4> and B=<−9,4,3>, what is A⋅B−||A||||B||?

1 Answer
Narad T.
Mar 4, 2018

The answer is =−87.5

Explanation:

The vectors are

→A=<3,1,−4>

→B=<−9,4,3>

The dot product is

→A.→B=<3,1,−4>.<−9,4,3>

=(3)⋅(−9)+(1)⋅(4)+(−4)⋅(3)

=−27+4−12

=−35

The magnitude of →A is

∣∣∣∣∣∣→A∣∣∣∣∣∣=||<3,1,−4>||

=√(3)2+(1)2+(−4)2

=√9+1+16

=√26

The magnitude of →B is

∣∣∣∣∣∣→B∣∣∣∣∣∣=||<−9,4,3>||

=√(9)2+(4)2+(3)2

=√81+16+9

=√106

Finally,

→A.→B−∣∣∣∣∣∣→A∣∣∣∣∣∣⋅∣∣∣∣∣∣→B∣∣∣∣∣∣=−35−√26⋅√106

=−35−52.5

=−87.5

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