34 use the given vectorUv nd w to find each expression U2i 3

(34) use the given vectorU.v nd w to find each expression

U=2i -3j+k

v=-3i+3j+2k

w=i+j+3k

v.(v.w)

Solution

U=2i -3j+k = (2 , -3 , 1)
v=-3i+3j+2k = (-3 , 3 , 2)
w=i+j+3k = (1 , 1 , 3)

v.(v.w) to be found

Answer :

v . <v . w>

<-3 , 3 , 2> <(-3 , 3 , 2) . (1 , 1 , 3)>

<-3 , 3, 2> < -3(1) + 3(1) + 2(3)>

<-3, 3 , 2> * 6

to get

<-18 , 18 , 12>

or in i,j,k format, this is

-18i + 18j + 12k -----> ANSWER