Question
Find the vector equation of the line passing through the point (1, 2, – 4) and perpendicular to the two lines:
Solution
Let a, b, c be the direction ratios of the line passing through the point (1, 2, – 4)
∴ equation of line is
...(1)
Since this line is perpendicular to the lines
and 3 a + 8 b – 5 c = 0
Solving these equations, we get,
∴ from (1), the equations of line is
∴ line passes through the point (1, 2, – 4) with position vector 
is parallel to 
.
∴ equation of line is
or 
