If #A= <2 ,-3 ,-4 ># and #B= <-1, -4, 2 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2016-02-06T23:41:38

#2-sqrt(609) ≈ -22.68#

Since #A • B=x_1x_2+y_1y_2+z_1z_2#, the #A • B# term equals #(2*-1) + (-3*-4) + (-4*2)#, which is 2.

Since the magnitude of a vector is given by #sqrt(x^2+y^2+z^2)#, the magnitude of A is #sqrt(2^2+(-3)^2+(-4)^2#, which equals #sqrt(29)#.

Likewise, the magnitude of B is #sqrt((-1)^2+(-4)^2+2^2#, which equals #sqrt(21)#

Therefore, the equation #A⋅B−||A||||B||# simplifies to #2-sqrt(29)*sqrt(21)# which further simplifies to #2-sqrt(609)#, which is approximately -22.68