If A= <3 ,1 ,-4 >A=<3,1,−4> and B= <-9 ,1 ,3 >B=<−9,1,3>, what is A*B -||A|| ||B||A⋅B−||A||||B||?

1 Answer
Shwetank Mauria
May 2, 2016

A*B-||A||||B||=-86.64A⋅B−||A||||B||=−86.64

Explanation:

As A=<3,1,-4>A=<3,1,−4> and B=<-9,1,3>B=<−9,1,3>

A*B=(3xx(-9)+1xx1+(-4)xx3)=(-27+1-12)=-38A⋅B=(3×(−9)+1×1+(−4)×3)=(−27+1−12)=−38

||A||||B||=sqrt(3^2+1^2+(-4)^2)xxsqrt((-9)^2+1^2+3^2)||A||||B||=√32+12+(−4)2×√(−9)2+12+32

= sqrt(9+1+16)xxsqrt(81+1+9)√9+1+16×√81+1+9

= sqrt26xxsqrt91√26×√91

= sqrt(2xx13xx13xx7)=13sqrt14=48.64√2×13×13×7=13√14=48.64

Hence A*B-||A||||B||=-38-48.64=-86.64A⋅B−||A||||B||=−38−48.64=−86.64

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