(Solved): (a) Find a vector equation of the line l which passes through the points P(1,-4,1) and Q(2,1,-2). ...

(a) Find a vector equation of the line

which passes through the points

and

. (b) Describe the line segment

(just the part of the line between

) by adding a condition to your answer in (a). (c) Does the point

lie on

? (d) What is the angle between

and

, where

is the origin? (e) Find a non-zero vector perpendicular to both

and

. (f) Write down a Cartesian equation for the plane

which passes through

and

. (g) Find the point of intersection of

and the line

.1. (a) Find a vector equation of the line ℓ which passes through the points P(1,−4,1) and Q(2,1,−2). (b) Describe the line segment PQ (just the part of the line between P & Q) by adding a condition to your answer in (a). (c) Does the point (5,17,−11) lie on ℓ? (d) What is the angle between OP andOQ, whereO is the origin? (e) Find a non-zero vector perpendicular to both OP and OQ. (f) Write down a Cartesian equation for the plane \phi which passes through P, Q and O. (g) Find the point of intersection of \phi and the line x = (−2,−6,6)+ t(0,−1,0), t in R