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# (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

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

(5,17,-11)

lie on

l

? (d) What is the angle between

OP

and

OQ

, where

O

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),tinR

.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

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