The angle between lines `(x-2)/(2)=(y-3)/(-2)=(z-5)/(1)` and `(x-2)/(1)=(y-3)/(2)=(z-5)/(2)` is . . . .

Options

A. `30^(@)`
B. `60^(@)`
C. `45^(@)`
D. `90^(@)`

Answer

D

Explanation

Key idea angle between lines
`(x-x_(1))/(a_(1))=(y-y_(1))/(b_(1))=(z-z_(1))/(c_(1)) and (x-x_(2))/(a_(2))=(y-y_(2))/(b_(2))=(z-z_(2))/(c_(2))` is given by `costheta=(|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)))`
Here, `a_(1)=2,b_(1)=-2,c_(1)=1`
and `a_(2)=1,b_(2)=2,c_(2)=2`
`thereforecostheta=(|2xx1+(-2)xx2+1xx2|)/(sqrt((2)^(2)+(-2)^(2)+(1)^(2))sqrt((1)^(2)+(2)^(2)+(2)^(2)))`
`implies cos theta=(|2-4+2|)/(sqrt(9)sqrt(9))=0impliestheta=(pi)/(2)`