The cosine of the angle of the triangle with vertices `A(1,-1,2),B(6,11,2)` and `C(1,2,6)` is

Options

A. `63/65`
B. `36/65`
C. `16/65`
D. `13/64`

Answer

B

Explanation

Direction ratios of
AB ` = ( 6-1, 11 + 1, 2 - 2 ) `
` = ( 5, 12, 0 ) `
Direction ratios of AC ` = ( 1 -1, 2 + 1, 6 - 2 ) `
` = ( 0 , 3,4 ) `
Now,
` cosA = (a _ 1 a _ 2 + b _ 1 b _ 2 + c _ 1 c _ 2 ) /( sqrt ( a _ 1 ^ 2 + b _ 1 ^ 2 + c_ 1 ^ 2 ) sqrt ( a _ 2 ^ 2 + b _ 2 ^ 2 + c _ 2 ^ 2 )) `
` rArr cos A = ( 5xx 0 + 12 xx 3 + 0 xx 4 ) /( sqrt ( 25 + 144 + 0 ) sqrt ( 0 + 9 + 16 ) ) `
` = ( 36 ) /(65 ) `