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(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`

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