The magnitude of the dot and cross product of two vectors 6 √3   and 6 respectively. Find the angle between the vectors. (Ans. 30°)


Given:

Let First vector is →A and second vector is →B then according to the given data

|→A . →B|= 6√3   ---------(1)
|→A ｘ →B|= 6  -------------(2)
 

To Find:

Angle between two vectors →A and →B  = θ =  ?

Solution:


In order to find θ between the two vectors, we will divide equation (2) by equation (1)

 |→Aｘ→B||→A.→B| =  66√3

or 

We know that

|→A . →B|=A B cos θ 
and
|→A ｘ →B|= A B sin θ 

So,


 ABsinθABcosθ =  66√3

Or

 sinθcosθ =  1√3

by simplifying 

tan θ =  1√3                               [  sinθcosθ = tan θ ]

Or

θ = tan⁻¹  1√3 

θ = 30°  ------------------Ans

Thus the angle between two vectors →A and →B  = θ =  30°


************************************

************************************

Shortcut Links For 


1. Website for School and College Level Physics   
2. Website for School and College Level Mathematics  
3. Website for Single National Curriculum Pakistan - All Subjects Notes 

© 2022-Onwards by Academic Skills and Knowledge (ASK)     

Note:  Write me in the comment box below for any query and also Share this information with your class-fellows and friends.