Question

If `A= <2 ,7 ,-4 >` and `B= <-2 ,-1 ,5 >`, what is `A*B -||A|| ||B||`?

Answer 1

`color(crimson)(- 71.2492)`

Explanation:

`"Dot Product or Scalar Product "`
`(a_1,a_2,a_3)·(b_1,b_2,b_3)=a_1b_1+a_2b_2+a_3b_3`

`"Vector Product " = abs(vec A) * abs(vec B)`

![https://sites.google.com/a/g.coppellisd.com/coppell-ib-math/math-sl/topics---sl/vectors/scalar-and-vector-product]()

`color(purple)(vecA·vecB=2 * -2 + 7 * -1 + -4·5=-31`

`color(blue)(abs(vecA)=sqrt(2^2+7^2+ -1^2)=sqrt 54`

`color(blue)(abs(vecB)=sqrt(-2^2+ -1^2+ 5^2)=sqrt 30`

Finally: `vecA·vecB-abs(vecA)·abs(vecB)=-21- sqrt54 sqrt 30`

`=> -31 -40.2492 =color(crimson)(-71.2492`