Question
Find the equations of the line passing through the point P(–1, 3, –2) and perpendicular to the lines
Solution
The equations of given lines are
...(1)
and
...(2)
Any line through P (– 1, 3, –2) is
...(3)
where l, m, n are direction ratios of the line
Since (3) is perpendicular to (1) and (2)
∴ l + 2 m + 3 n = 0 ...(4)
and – 3 l + 2 m + 5 n = 0 ...(5)
Solving (4) and (5), we get,
...(1)and
...(2)Any line through P (– 1, 3, –2) is
...(3)where l, m, n are direction ratios of the line
Since (3) is perpendicular to (1) and (2)
∴ l + 2 m + 3 n = 0 ...(4)
and – 3 l + 2 m + 5 n = 0 ...(5)
Solving (4) and (5), we get,
∴ from (3), the equations of line are
