Under what condition are the two lines
`y=m/lx+alpha,z=n/lx+beta, and y=(m')/(l')x+alpha',z=(n')/(l')x+beta'`orthogonal?

Prove that the straight lines x/alpha=y/beta=z/gamma,x/l=y/m=z/n and x/(a alpha)=y/(b beta)=z/(c gamma) will be co planar if l/alpha(b-c)+m/beta(c-a)+n/gamma(a-b)=0

Prove that the straight lines x/alpha=y/beta=z/gamma,x/l=y/m=z/n and x/(a alpha)=y/(b beta)=z/(c gamma) will be co planar if l/alpha(b-c)+m/beta(c-a)+n/gamma(a-b)=0

Find the equation to the plane through the line (x - alpha)/(l) = (y - beta)/(m) = (z -gamma)/(n) and parallel to the line (x)/(l') = (y)/(m') = (z)/(n') .

The two lines lx+my=n and llx+m'y=n' are perpendicular if

Find the equation to the plane through the line (x-alpha)/l=(y-beta)/m=(z-gamma)/n and parallel to the line x/(l')=y/(m')=z/(n')

Statement -I : A line makes the same angle theta with each of the x and z-axis. If it makes an angle alpha with the y-axis, such that sin^(2) alpha=3 sin^(2) theta , then cos^(2) theta=3/5 . Statement -II : If a line with direction ratios, l, m, n makes angles alpha, beta, gamma respectively with x, y amd z-axis then cos alpha=(l)/sqrt(l^(2)+m^(2)+n^(2)), cos beta =(m)/sqrt(l^(2)+m^(2)+n^(2)) and cos gamma =(n)/sqrt(l^(2)+m^(2)+n^(2)) .