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

1 Answer
Narad T.
Dec 5, 2017

The answer is =−9.25

Explanation:

The vectors are

→A=<−2,3,3>

→B=<−9,2,8>

The modulus of →A is =∣∣∣∣∣∣→A∣∣∣∣∣∣=||<−2,3,3>||=√(−2)2+(3)2+(3)2=√4+9+9=√22

The modulus of →B is =∣∣∣∣∣∣→B∣∣∣∣∣∣=||<−9,2,8>||=√(−9)2+(2)2+82=√81+4+64=√149

Therefore,

∣∣∣∣∣∣→A∣∣∣∣∣∣×∣∣∣∣∣∣→B∣∣∣∣∣∣=√22⋅√149=√3278

The dot product is

→A.→B=<−2,3,3>.<−9,2,8>=(−2×−9)+(3×2)+(3×8)=18+6+24=48

Therefore,

→A.→B−∣∣∣∣∣∣→A∣∣∣∣∣∣×∣∣∣∣∣∣→B∣∣∣∣∣∣=48−√3278=−9.25

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