If A=<6,−5,3> and B=<−7,4,−9>, what is A⋅B−||A||||B||?

1 Answer
Narad T.
Dec 17, 2017

The answer is =−190.1

Explanation:

The vectors are

→A=<6,−5,3>

→B=<−7,4,−9>

The modulus of →A is =∣∣∣∣∣∣→A∣∣∣∣∣∣=||<6,−5,3>||=√(6)2+(−5)2+(3)2=√36+25+9=√70

The modulus of →B is =∣∣∣∣∣∣→B∣∣∣∣∣∣=||<−7,4,−9>||=√(−7)2+(4)2+(−9)2=√49+16+81=√146

Therefore,

∣∣∣∣∣∣→A∣∣∣∣∣∣⋅∣∣∣∣∣∣→B∣∣∣∣∣∣=√70⋅√146=√10220

The dot product is

→A.→B=<6,−5,3>.<−7,4,−9>=(6×−7)+(−5×4)+(3×−9)=−42−20−27=−89

Therefore,

→A.→B−∣∣∣∣∣∣→A∣∣∣∣∣∣×∣∣∣∣∣∣→B∣∣∣∣∣∣=−89−√10220=−190.1

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