If #A= <4, 0 ,-3 ># and #B= <-2 ,5 ,7 >#, what is #A*B -||A|| ||B||#?

1 Answer
Nov 27, 2016

The answer is #=-29-5sqrt78=-53.2#

Explanation:

Let #vecA=〈a_1,a_2,a_3〉#

and #vecB=〈b_1,b_2,b_3〉#

The dot product is

#vecA.vecB=〈a_1,a_2,a_3〉.〈b_1,b_2,b_3〉#

#=a_1b_1+a_2b_2+a_3b_3#

and the modulus is

#∥vecA∥=sqrt(a_1^2+a_2^2+a_3^2)#

#∥vecB∥=sqrt(b_1^2+b_2^2+b_3^2)#

Here, #vecA=〈4,0,-3〉#

and #vecB=〈-2,5,7〉#

#vecA.vecB=-8+0-21=-29#

#∥vecA∥=sqrt(16+0+9)=sqrt25=5#

#∥vecB∥=sqrt(4+25+49)=sqrt78#

Therefore,

#vecA.vecB-∥vecA∥∥vecB∥=-29-5sqrt78=-53.2#