Question

a = (0,1,2) b=(1,1,1) c= (2,1,0)

(a) evalute the folowing binary and triple combination of vectors (i) b*c ((ii) c x b (iii) a*(bxc)

(b) Detremine the angle between vectors a and b.

Answer 1

Given, a = (0,1,2), b = (1,1,1), c = (2,1,0)

a) i) b*c = (1,1,1)*(2,1,0)

i.e., b*c = (1*2)+(1*1)+(1*0)

i.e., b*c = 2+1+0

i.e., b*c = 3

ii) c x b = (2,1,0) x (1,1,1)

i.e., c x b = ([1*1-0*1],[0*1-2*1],[2*1-1*1])

i.e., c x b = ((1-0),(0-2),(2-1))

i.e., c x b = (1,-2,1)

iii) Here, b x c = -(c x b)

i.e., b x c = (-1,2,-1)

Now, a*(b x c) = (0,1,2)*(-1,2,-1)

i.e., a*(b x c) = 0*(-1)+1*2+2*(-1)

i.e., a*(b x c) = 0+2-2

i.e., a*(b x c) = 0

b) If theta be the angle between a and b, then
Therefore, angle between a and b is 39.23^o.