The acute angle between the line `(x+1)/(2) = (y)/(3)= (z-3)/(6)` and the plane `10 x + 2y -11z = 8` is

Options

A. `sin^(-1)((8)/(21))`
B. `cos^(-1)((8)/(21))`
C. `sin^(-1)((1)/(8))`
D. `cos^(-1)((1)/(8))`

Answer

A

Explanation

`sintheta=(aa_(1)+bb_(1)+c""c_(1))/(sqrt(a^(2)+b^(2)+c^(2)).sqrt(a_(1)^(2)+b_(1)^(2)+c_(1)^(2)))`
`=(10xx2+2+3+(-11)xx6)/(sqrt(10^(2)+2^(2)+(-11)^(2)).sqrt(2^(2)+3^(2)+6^(2)))`
`=(-40)/(sqrt225xxsqrt(49))`
`=(-40)/(15xx7)=(-8)/(21)`
`:.theta=sin^(-1)((-8)/(21))`
`:.theta=sin^(-1)((-8)/(21))` `:'theta` is an acute angle.