Calculate the dot products of the following vectors Tell whi

Calculate the dot products of the following vectors. Tell which pairs are orthogonal. [2,1]-[-1, 2] [2,1, 2].[3,-1,0] [5, 7, 5,1]. [-2,4,-3,-3]

Solution

Dot product of [a,b][x,y] = (a*x) + (b*y)

(a) [2,1].[-1,2] = (2)(-1) + (1)(-1)

= (-1) + (-1)

= -2

(b) [2,1,2].[3,-1,0] = (2*3)+(1*-1)+(2*0)

= 6 + (-1)

= 5

(c) [5,7,5,1].[-2,4,-3,-3] = (5*-2)+(7*4)+(5*-3)+(1*-3)

= -10+28-15-3

= 0 which satisfied the orthogonal condition so it is pair of orthogonal

Answer