If #A= <16 ,-4 ,-1 ># and #B= <2 ,-9 ,3 >#, what is #A*B -||A|| ||B||#?

1 Answer
Faizan B.
Feb 6, 2016

#65-sqrt(25662) ≈ -95.19#

Explanation:

Since #A • B=x_1x_2+y_1y_2+z_1z_2#, the #A • B# term equals #(16*2) + (-4*-9) + (-1*3)#, which is 65.

Since the magnitude of a vector is given by #sqrt(x^2+y^2+z^2)#, the magnitude of A is #sqrt(16^2+(-4)^2+(-1)^2#, which equals #sqrt(273)#.

Likewise, the magnitude of B is #sqrt(2^2+(-9)^2+(3)^2#, which equals #sqrt(94)#

Therefore, the equation #A⋅B−||A||||B||# simplifies to #65-sqrt(273)*sqrt(94)# which further simplifies to #65-sqrt(25662)#, which is approximately -95.19

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