The angle between two vectors given by `6 hati + 6 hatj - 3 hatk and 7 hati + 4 hatj + 4 hatk ` is :-

Options

A. `cos ^(-1) ((1)/( sqrt(3)))`
B. `cos ^(-1) ((5)/(3))`
C. `sin ^(-1) ( (2)/( sqrt(3)))`
D. `sin ^(-1) ((sqrt""5)/(3))`

Answer

D

Explanation

`cos theta = ( vecA . vecB )/(AB) = (( 6 hati + 6 hatj - 3 hatk ).( 7 hati + 4 hatj + 4 hatk ))/( sqrt(6)^2 +6^(2) +3^(2) sqrt(7) +4 ^(2) + 4 ^(2))`
` cos theta = ( 42+24-12 )/( 9xx9 ) =( 54 )/( 9xx9 ) =(2)/(3)`
` sin theta = sqrt(1- cos ^(2) theta ) = ( sqrt(5))/(3)`