If A= <-2 ,3 ,-4 >A=<−2,3,−4> and B= <-9 ,4 ,8 >B=<−9,4,8>, what is A*B -||A|| ||B||A⋅B−||A||||B||?

1 Answer
Narad T.
Jan 4, 2018

The answer is =-70.3=−70.3

Explanation:

The dot product is

A.B= <-2,3,-4> . <-9,4,8> = (-2*-9)+(3*4)+(-4*8) =18+12-32= -2A.B=<−2,3,−4>.<−9,4,8>=(−2⋅−9)+(3⋅4)+(−4⋅8)=18+12−32=−2

The modulus of vecA→A is

=||vecA|| =|| <-2,3,-4> || =sqrt((-2)^2+(3)^3+(-4)^2)=sqrt(4+9+16)=sqrt(29)=∣∣∣∣∣∣→A∣∣∣∣∣∣=||<−2,3,−4>||=√(−2)2+(3)3+(−4)2=√4+9+16=√29

The modulus of vecB→B is

=||vecB|| =|| <-9,4,8> || =sqrt((-9)^2+(4)^3+(8)^2)=sqrt(81+16+64)=sqrt(161)=∣∣∣∣∣∣→B∣∣∣∣∣∣=||<−9,4,8>||=√(−9)2+(4)3+(8)2=√81+16+64=√161

Therefore,

A.B-||vecA||*||vecB||=-2-sqrt29*sqrt161=-70.3A.B−∣∣∣∣∣∣→A∣∣∣∣∣∣⋅∣∣∣∣∣∣→B∣∣∣∣∣∣=−2−√29⋅√161=−70.3

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