If A=<−5,−1,−3> and B=<−6,−4,−7>, what is A⋅B−||A||||B||?

1 Answer
Narad T.
Nov 27, 2017

The answer is =4.46

Explanation:

The vectors are

→A=<−5,−1,−3>

→B=<−6,−4,−7>

The modulus of →A is =∣∣∣∣∣∣→A∣∣∣∣∣∣=||<−5,−1,−3>||=√(−5)2+(−1)2+(−3)2=√25+1+9=√35

The modulus of →B is =∣∣∣∣∣∣→B∣∣∣∣∣∣=||<−6,−4,−7>||=√(−6)2+(−4)2+(−7)2=√36+16+49=√101

Therefore,

∣∣∣∣∣∣→A∣∣∣∣∣∣⋅∣∣∣∣∣∣→B∣∣∣∣∣∣=√35⋅√101=√3535

The dot product is

→A.→B=<−5,−1,−3>.<−6,−4,−7>

=(−5×−6)+(−1×−4)+(−3×−7)

=30+4+21=55

Therefore,

→A.→B−∣∣∣∣∣∣→A∣∣∣∣∣∣×∣∣∣∣∣∣→B∣∣∣∣∣∣=55−√3535=−4.46

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