Question
Show that, if the axes are rectangular, then the equations of the line through (α, β, γ) right angles to the lines
are 
Solution
The equations of given lines are
...(1)
and
...(2)
Any line through (α, β, γ) is
where l, m, n are direction-ratios of the line
Since (3) is perpendicular to (1)
∴ l l1 + m m1 + n n1 = 0 ....(4)
Since (3) is perpendicular to (2)
∴ I l2 + m m2 + n n2 = 0
Solving (4) and (5), we get,
∴ from (3), the equations of line are
...(1)and
...(2)Any line through (α, β, γ) is
where l, m, n are direction-ratios of the line
Since (3) is perpendicular to (1)
∴ l l1 + m m1 + n n1 = 0 ....(4)
Since (3) is perpendicular to (2)
∴ I l2 + m m2 + n n2 = 0
Solving (4) and (5), we get,
∴ from (3), the equations of line are
