The diection cosines of two lines are proportional to `(2,3,-6) and (3,-4,5),` then the acute angle between them is

Options

A. `cos^(-1)((49)/(36))`
B. `cos^(-1)(6/(35sqrt2))`
C. `96^@`
D. `cos^(-1)((18)/(35))`

Answer

B

Explanation

Since, direction cosines of two lines are proportional to (2,3,-6) and (3,-4,5)
`thereforecostheta=(|2xx3+3xx(-4)-6xx5|)/(sqrt(2^2+3^2+(-6)^2)sqrt(3^2+(-4)^2+5^2))`
`=(|6-12-30|)/(sqrt(49)sqrt(50))rArrtheta=cos^(-1)""(6/(35sqrt(2)))`