Given the vectors #u=<2,2>#, #v=<-3,4>#, and #w=<1,-2>#, how do you find #u*u#?

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Answer 1 · 2018-07-01T10:07:10

# = 8 #

If #a = < a_1 , a_2 > #

and #b = < b_1 , b_2 > #

#=> a * b = a_1b_1 + a_2b_2 #

In general

#v,u in RR^n #

#u = < a_1 , a_2 , ... , a_n >#

#v = < b_1 , b_2 , ... , b_n >#

#=> u * v = sum_(i = 1) ^n a_i b_i #

In this case:

# = <2,2> * <2,2> = (2*2) + (2*2) = 8 #