what is the angle between the lines x+z=0,y=0 and 20x=15y=12z?

Options

A. `cos^(-1)(1//5)`
B. `cos^(-1)(1//7)`
C. `cos^(-1)45/(7sqrt61)`
D. `sin^(-1)(1//7)`

Answer

A

Explanation

Given, `c+z=0,y=0 and 20x=15y=12z`
`rArr x/1=y/0=z/(-1) and x/3=y/4=z/5`
Let `theta` be angle between two lines.
`:. costheta=abs(((1)(3)+(0))/sqrt(1+0+1)((4)+(-1)(5))/sqrt(9+16+25))=abs((3+0-5)/(sqrt2sqrt20))`
`=2/(sqrt2. 5sqrt2)=1/5`
`:. theta=cos^(-1)(1/5)`