If #A= <-5 ,3 ,-7 ># and #B= <2 ,-9 ,8 >#, what is #A*B -||A|| ||B||#?

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Answer 1 · 2016-11-18T16:14:54

The answer is #=-204.2#

We start by calculating the dot product.

#vecA.vecB=〈-5,3,-7〉〈2,-9,8〉#

#=(-5*2)+(3*-9)+(8*-7)#

#=-10-27-56=-93#

Now, we calculate the modulus.

The modulus of #vecA=∥〈-5,3,-7〉∥=sqrt(25+9+49)#

#=sqrt83#

The modulus of #vecB=∥〈2,-9,8〉∥= sqrt(4+81+64)#

#=sqrt149#

#vecA.vecB-∥vecA∥*∥vecB∥=-93-sqrt(83*149)=-204.2#