If IA×B| = A•B, what is the angle between A and B?

Asked by gkgoraya445 | 21st Aug, 2020, 08:13: PM

Expert Answer:

Vector product of two vectors A and B is,  
 
open vertical bar A cross times B close vertical bar space equals space open vertical bar A close vertical bar open vertical bar B close vertical bar space sin theta
D o t space p r o d u c t space o f space t w o space v e c t o r space A space a n d space B space a r e space e x p r e s s e d space a s comma space
open vertical bar A. B close vertical bar equals space space open vertical bar A close vertical bar open vertical bar B close vertical bar space cos theta
I t space i s space g i v e n space t h a t comma space
open vertical bar A cross times B close vertical bar space equals space open vertical bar A. B close vertical bar... left parenthesis g i v e n right parenthesis
T h u s comma space
space open vertical bar A close vertical bar open vertical bar B close vertical bar space sin theta space equals space open vertical bar A close vertical bar open vertical bar B close vertical bar space cos theta
rightwards double arrow sin theta space equals space cos theta
rightwards double arrow tan theta space equals space 1
therefore theta space equals tan to the power of negative 1 end exponent open parentheses 1 close parentheses space equals space 45 degree 
Thus, the angle between A and B is 45°

Answered by Shiwani Sawant | 21st Aug, 2020, 09:18: PM