The line L passes through the point A, whose position vector is i-j-5k and is parrallel to the vector i-j-4k. The line l2 passes through the point B, whose position vector is 2i-9j-14k, and is parrallel to the vector 2i+5j+6k. The point L and the point Q on L2 are such that PQ is perpendicular to both L and L2.
a. Find the length of PQ
b. Find a vector perpendicular to the plane which contains PQ and L2.
c. Find the perpendicular distance from A to the plane.
Hello, kingkaisai2!
Here's my approach to part (a).
. . But I'm sure there's a better way!
The line passes through the point
. . and is parallel to the vector
The line passes through the point
. . and is parallel to the vector
The point on and the point on are such that
. . and
(a) Find the length of
Line has parametric equations; .
Line has parametric equations: .
The vector perpendicular to both and is given by:
. .
We have: . and
. . and we want: .
So we have: .
. . . . . . . . . .
And we have: .
Solve the system of equations: .
Hence: . and
Therefore: .