Question

t) Let a , b , c and y be the three dimensional vectors
a =4j +2k ,b =−3i +4j +4k ,c =3i −j ,y =8i −7j
Perform the following operations on these vectors:
(a) c⋅a +a⋅y =
(b) (a ⋅b )a =
(c) ((c⋅c)a )⋅a =

Answer 1

I will try one. You try the rest.
c dot a = 3i − 1j + 0 k dot 0 i + 4j + 2k = 3*0-4*1 +0*2 = -4
a dot y = 0 i + 4j + 2k dot 8 i -7j + 0k = 0*8 -4*7 +2*0 = - 28
so -32

Answer 2

a=<0,4,2> , b=<-3,4,4> , c=<3,-1,0> and y=<8,-7,0>

I will do b)
you do the rest and let me know what you got

b) (a ⋅b )a
= (0 + 16 + 8)<0,4,2> , which is a scalar times a vector
= 24<0,4,2>
= <0,96,48>

Answer 3

LOL , well Carl better do the last one !