The diection cosines of two lines are proportional to `(2,3,-6) and (3,-4,5),` then the acute angle between them is (A) `cos^-1{49/36}` (B) `cos^-1 {(18sqrt(2))/35}` (C) `96^0` (D) `cos^-1(18/35)`

Options

A. `"cos"^(-1)((49)/(36))`
B. `"cos"^(-1)((18sqrt(2))/(35))`
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)
`costheta=(|2xx3+3xx(-4)-6xx5|)/(sqrt(2^(2)+3^(2)+(-6)^(2)))`
`sqrt(3^(2)+(-4)^(2)+5^(2))`
`=(|6-12-13|)/(sqrt(49)sqrt(50))`
`impliestheta=cos^(-1)((18sqrt(2))/(35))`