If #A= <8 ,- 2 ,9># and #B= <5 ,1 ,0 >#, what is #A*B -||A|| ||B||#?

1 Answer
Feb 6, 2016

#65-sqrt(3874) ≈ 2.76#

Explanation:

Since #A • B=x_1x_2+y_1y_2+z_1z_2#, the #A • B# term equals #(8*5) + (-2*1) + (9*0)#, which is 38.

Since the magnitude of a vector is given by #sqrt(x^2+y^2+z^2)#, the magnitude of A is #sqrt(8^2+(-2)^2+9^2#, which equals #sqrt(149)#.

Likewise, the magnitude of B is #sqrt(5^2+1^2+0^2#, which equals #sqrt(26)#

Therefore, the equation #A⋅B−||A||||B||# simplifies to #38-sqrt(149)*sqrt(26)# which further simplifies to #65-sqrt(3874)#, which is approximately 2.76