If #A= <8 ,-5 ,1 ># and #B= <4 ,1 ,3 >#, what is #A*B -||A|| ||B||#?

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If #A= <8 ,-5 ,1 ># and #B= <4 ,1 ,3 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2018-02-05T13:47:55

#6(5-sqrt65)#
See details below

Explanation:

#absA=sqrt(a_1^2+a_2^2+a_3^2#=#sqrt(8^2+5^2+1^2#=#sqrt90#=#3sqrt10#
#absB#=#sqrt(4^2+1^2+3^2#=#sqrt26#
#A·B#=#a_1b_1+a_2b_2+a_3b_3# = #32-5+3=30#
Thus:
#A·B-absAabsB#=#30-3sqrt10sqrt26#=#6(5-sqrt65)#

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If #A= <8 ,-5 ,1 ># and #B= <4 ,1 ,3 >#, what is #A*B -||A|| ||B||#?

1 Answer

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