If A=<−5,3,−7> and B=<2,2,8>, what is A⋅B−||A||||B||?

1 Answer
Narad T.
Jun 21, 2017

The answer is =−137.3

Explanation:

The dot product is

→A.→B=<−5,3,−7>.<2,2,8>

=−10+6−56=−60

The magnitude of →A is

=∣∣∣∣∣∣→A∣∣∣∣∣∣=||<−5,3,−7>||=√(−5)2+(3)2+(−7)2

=√25+9+49=√83

The magnitude of →B is

=∣∣∣∣∣∣→B∣∣∣∣∣∣=||<2,2,8>||=√(2)2+(2)2+(8)2

=√4+4+64=√72

Therefore,

→A.→B−∣∣∣∣∣∣→A∣∣∣∣∣∣⋅∣∣∣∣∣∣→B∣∣∣∣∣∣=−60−√83√72

=−137.3

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