Question

Given that :
r−1=6i−8j+2k, r2=4i+5j+7k, r3=−2i+j+6k is a vector.Findr1r2

Answer 1

Task. Given that:

$r_{1}=6i-8j+2k,\qquad r_{2}=4i+5j+7k,\qquad r_{3}=-2i+j+6k$

Find $(r_{1},r_{2})$.

Solution. The scalar product $(r_{1},r_{2})$ of vectors

$r_{1}=a_{1}i+a_{2}j+a_{3}k,\qquad r_{2}=b_{1}i+b_{2}j+b_{3}k,$

can be computed by the following formula:

$(r_{1},r_{2})=a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}.$

In our case

$r_{1}=6i-8j+2k,\qquad r_{2}=4i+5j+7k$

and so

$a_{1}=6,\qquad a_{2}=-8,\qquad a_{3}=2$

$b_{1}=4,\qquad b_{2}=5,\qquad b_{3}=7$

Substituting values we get

$(r_{1},r_{2})=a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}=6*4+(-8)*5+2*7=24-40+14=-2.$

Answer. $(r_{1},r_{2})=-2.$