Question

prove that vector A=i plus 2j plus 3k and B=2i minus j

Answer 1

both are perpendicular vectors because their dot product is 0
A= i+2j+3k B=2i-j
their dot product is A.B = i.2i + 2j.-j + 3k.0 = 2-2 =0

Answer 2

A = î +2j + 3k
B = 2î - j

Now, A.B = (1*2) + (2*-1) + (3*0)
=> |A|.|B|.cosθ = 2 - 2 = 0
It means either |A|.|B| = 0 or cosθ = 0
But magnitude can never be zero.
=> |A|.|B| ≠ 0
=> cosθ = 0
=> cosθ = cos 90°
=> θ = 90°
Hence, vector A is perpendicular to vector B.


hope it helps ........