If #A= <-3 ,3 ,-1 ># and #B= <8 ,7 ,2 >#, what is #A*B -||A|| ||B||#?

1 Answer
Faizan B.
Feb 6, 2016

#-5-sqrt(2223) ≈ -52.15#

Explanation:

Since #A • B=x_1x_2+y_1y_2+z_1z_2#, the #A • B# term equals #(-3*8) + (3*7) + (-1*2)#, which is -5.

Since the magnitude of a vector is given by #sqrt(x^2+y^2+z^2)#, the magnitude of A is #sqrt((-3)^2+(3)^2+(-1)^2#, which equals #sqrt(19)#.

Likewise, the magnitude of B is #sqrt(8^2+7^2+2^2#, which equals #sqrt(117)#

Therefore, the equation #A⋅B−||A||||B||# simplifies to #-5-sqrt(19)*sqrt(117)# which further simplifies to #-5-sqrt(2223)#, which is approximately -52.15

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