How do I solve the following?

Question

Use the vectors u = <2, 2>, v = <-3, 4> and w = <1, -2> to find the indicated quantity.
a) 3u ∙ v

b) (u ∙ 2v)w

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Answer 1 · 2018-02-16T05:31:54

The solution is given below ;-

a) #3vecu.vecv# #=# #3(2hati# #+# #2hatj##)#.#(-3hati + 4hatj)#

#rArr 3vecu.vecv = 3(-6 + 8) = 6#

b) #(vecu.2vecv)vecw = 2(vecu.vecv)vecw = #

#2{(2hati+2hatj).(-3hati + 4hatj)}(hati-2hatj)#

#rArr(vecu.2vecv)vecw = 4(hati-2hatj) = 4hati-8hatj#