The angle betweenthe lines whose direction cosines satisfy the equations `l+m+n=""0`and `l^2=m^2+n^2`is(1) `pi/3`(2) `pi/4`(3) `pi/6`(4) `pi/2`A. `(pi)/(3)`B. `(pi)/(4)`C. `(pi)/(6)`D. `(pi)/(2)`

The angle betweenthe lines whose direction cosines satisfy the equatio

1.	The angle betweenthe lines whose direction cosines satisfy the equations `l+m+n=""0`and `l^2=m^2+n^2`is(1) `pi/3`(2) `pi/4`(3) `pi/6`(4) `pi/2`A. `(pi)/(3)`B. `(pi)/(4)`C. `(pi)/(6)`D. `(pi)/(2)`
Answer» Correct Answer - A We know that, angle between two lines is `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)))` `l+m+n=0` `implies" "l=-(m+n)implies(m+n)^(2)=l^(2)` `implies" "m^(2)+n^(2)+2mn=m^(2)+n^(2)" "[becausel^(2)=m^(2)+n^(2)," given"]` `implies" "2mn=0` When `" "m=0` `implies" "l=-n` Hence, (l, m, n) is (1, 0, -1). When `" "n=0," then "l=-m` Hence, (l, m, n) is (1, 0, -1). `:.costheta=(1+0+0)/(sqrt(2)xxsqrt(2))=(1)/(2)impliestheta=(pi)/(3)`

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