Find the distance of the point from the line measured parallel to the plane
Step 1:Find the general co-ordinates of a point on the given line
Let (say)
………………………(1)
Let us consider.
Let be the plane parallel to the given plane through
let be the point where the given line intersects.
Step 2:Solve for the equation of
We know that is parallel to the given plane so the equation of which differs only in the constant term.
Where is a constant
Since point lies on the plane , its co-ordinates satisfy the equation of the plane
So the equation for is
……………………..(2)
Step 3: Solve for point which lies on the plane and the given line
General co-ordinates of a point on the given line are
…[From(1)]
These co-ordinates satisfy the equation of plane
Hence, substituting the values of from (1) in (2) we get
Resubstituting the value of we get
Step 4: Find the length of:
We know and
Length of
Length of
The distance between coordinates and is unit.
Hence, the distance between the point and the given line passing parallel to the given plane is unit