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The angle betweeen the lines x/1=y/0=z/(...

The angle betweeen the lines `x/1=y/0=z/(-1)and x/3=y/4=z/5` is equal to

A

`pi-cos^(-1)((1)/(5))`

B

`cos^(-1)((1)/(3))`

C

`cos^(-1)((1)/(2))`

D

`cos^(-1)((1)/(4))`

Text Solution

Verified by Experts

The correct Answer is:
A
`therefore cos theta=(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))`
`therefore cos theta =(1xx3+0xx4-1xx5)/(sqrt(1+0+1)sqrt(9+16+25))`
`=(-2)/(sqrt2sqrt50)=(-2)/(2xx5)=-1/5`
`therefore theta=pi-cos^(-1)((1)/(5))`
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