If A=<−2,−7,−1> and B=<3,4,−8>, what is A⋅B−||A||||B||?

1 Answer
Narad T. · Shwetank Mauria
Dec 14, 2017

The answer is =−95.3

Explanation:

The vectors are

→A=<−2,−7,−1>

→B=<3,4,−8>

The modulus of →A is =∣∣∣∣∣∣→A∣∣∣∣∣∣=||<−2,−7,−1>||=√(−2)2+(−7)2+(−1)2=√4+49+1=√54

The modulus of →B is =∣∣∣∣∣∣→B∣∣∣∣∣∣=||<3,4,−8>||=√(3)2+(4)2+(−8)2=√9+16+64=√89

Therefore,

∣∣∣∣∣∣→A∣∣∣∣∣∣×∣∣∣∣∣∣→B∣∣∣∣∣∣=√54⋅√89=√4806

The dot product is

→A.→B=<−2,−7,−1>.<3,4,−8>=(−2×3)+(−7×4)+(−1×−8)=−6−28+8=−26

Therefore,

→A.→B−∣∣∣∣∣∣→A∣∣∣∣∣∣×∣∣∣∣∣∣→B∣∣∣∣∣∣=−26−√4806=−95.3

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