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

1 Answer
Faizan B.
Feb 6, 2016

#33-sqrt(2516) ≈ -17.16#

Explanation:

Since #A • B=x_1x_2+y_1y_2+z_1z_2#, the #A • B# term equals #(-8*-3) + (3*4) + (-1*3)#, which is 33.

Since the magnitude of a vector is given by #sqrt(x^2+y^2+z^2)#, the magnitude of A is #sqrt((-8)^2+3^2+(-1)^2#, which equals #sqrt(74)#.

Likewise, the magnitude of B is #sqrt((-3)^2+4^2+3^2#, which equals #sqrt(34)#

Therefore, the equation #A⋅B−||A||||B||# simplifies to #33-sqrt(74)*sqrt(34)# which further simplifies to #33-sqrt(2516)#, which is approximately -17.16

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