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if i, j, k be unit orthonormal vectors and a be any, also a×r=j then a.r is equal to (1)0 (2)1 (3)-1 (4) Arbitrary scalar

if i, j, k be unit orthonormal vectors and a be any, also a×r=j then a.r is equal to (1)0 (2)1 (3)-1 (4) Arbitrary scalar

Grade:12

1 Answers

Arun
25763 Points
4 years ago
We have 
|a x r|² + |a.r|² = |a|² |r|²
| j|² + (a. r)² = |a|² |r|²
(a. r) = + - \sqrt(|a|² |r|² - 1)
 
This shows that (a. r) depends on |r | on a given a.
 
Hence (a.r) is  any arbitrary scalar.
Option D is correct.
 
Regards
Arun(askIITians forum expert)

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