Question
The cartesian equations of a line are 6 x – 2 = – 3 y + 1 = 2 z = 2. Find the direction ratios of the line and write down the vector equation of the line through (2, – 1, –1) which is parallel to the given line.
Solution
The equation of the line are 6 x – 2 = 3 y + 1 = 2 z – 2
or
or
∴ direction-ratios of the line are 1, 2, 3.
Required line passes through (2, – 1, – 1)
Let
be the position vector of any point on the line.
∴ the vector equation of required line is
where λ is a parameter.
or
or
∴ direction-ratios of the line are 1, 2, 3.
Required line passes through (2, – 1, – 1)
Let
be the position vector of any point on the line. ∴ the vector equation of required line is
where λ is a parameter.
