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Grade: 12
        
The sum,diiference and cross product of two vectors A and B are mutually perpendicular if there magnitude are same and directions are arbitrary.Prove the above statement.
 
 
 
 
 
 
 
 
 
one year ago

Answers : (1)

Arun
23506 Points
							

Let's consider the following cross product

(A + B) X (A - B)

if the two ar mutually perpendicular then Cosα (where α is the angle between them) would be zero

so,

(A + B) X (A - B) = 0

thus 

(A X A) - (B X B) - (A X B) + (B X A) = 0

or

A2 - B2 = 0  ( A X B = - B X A )

thus, we get

A = B

or

A = B

so the two vectors are equal in magnitude

one year ago
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