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CBSE Class 11-science Answered

If IA×B| = A•B, what is the angle between A and B?
Asked by gkgoraya445 | 21 Aug, 2020, 20:13: PM
answered-by-expert 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 | 21 Aug, 2020, 21:18: PM

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