A line with directiion ratios 2, 7, -5 is intercepted between the lines
x−53=y−7−1=z+21 and x+3−3=y−32=z−64. Find the length intercepted between the given lines.
The general points on the given lines are respectively
Direction numbers of PQ are
If PQ is the desired line then direction numbers of PQ should be proportional to < 2, 7, -5> therefore,
Taking first and second numbers, we get
taking second and third member, we get
Solving (i) and (ii) for t and s we get
s=−1 and t=−1. The coordinates of P and Q are respectively
∴ the said line intersects the given lines in the points (2,8,−3) and (0,1,2) respectively.
Length of the line intercepted between the given lines