Question

What is the angle between the following two vectors: [111] and [010] Ο 60° Ο 30° Ο 54.70 Ο 45ο

Answer 1

Ans :

  $\small \dot{u}$ = [ 1 1 1 } &  $\small \dot{v}$ = [ 0 1 0]

Angle between two vectors $\small \ddot{}$ $\small \dot{u}$ & $\small \dot{v}$ is given by

cos $\small \Theta$ = u .v / II$\small \dot{u}$II II $\small \dot{v}$ II

II$\small \dot{u}$II = Magnitude of  $\small \dot{u}$ = $\small \sqrt{1^{2}+1^{2}+1^{2}}$ =  $\small \sqrt{3}$  

II$\small \dot{v}$II = Magnitude of $\small \dot{v}$    = $\small \sqrt{0^{2}+1^{2}+0^{2}}$ = $\small \sqrt{1}$ = 1

Dot product of  $\small \dot{u}$ & $\small \dot{v}$

u .v = (1 x1x1 ) + (0 x 1 x0)  

= 1 + 0 = 1

Using formula for angle

cos $\small \Theta$ = 1 / ( $\small \sqrt{3}$ x  1 )

= 1 / $\small \sqrt{3}$

Therefore $\small \Theta$ = cos-1  (1 / $\small \sqrt{3}$ )

= 54.7350

Angle between two vectors = 54.70  ( Rounding off )