equation of line and plane !! plzzzz help

Re: equation of line and plane !! plzzzz help

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**alakd** Can someone help with this multi-part question. i did the first three but it doesnt seem right!

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(a) Find the equation of the line l through P(1, 1, 2) and Q(1, 0, 4) in vector, parametric and Cartesian forms.

(b) Find the vector form of the line k through R(0, 3, 1) which is perpendicular to l.

(c) Find the Cartesian form of the plane containing the lines l and k.

(d) Find the vector form of the line through T(0, 0, 3) which is normal to this plane.

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so i guess i did the first bit alright : cartesian : z=6+4x , y=6

for the second one i got this line : (-5,4,2)+t(28,-37,7) , i timed it by 17 to get rid of the denominator

third part : the lines seem to have no intersection so i am stuck!

appreciate it if anyone can help out

The line will be infinitely long and in the direction of the vector that goes from to . So

To make it infinitely long, we multiply by some parameter, , to give .

Then we need to position this infinitely long vector at a point. Adding either of the points you know the line goes through will do.

So .

This is the vector form of the line.

To get the parametric equations, expand it out...

To get the Cartesian equations, try to write each of them as t in terms of the other variable and set them equal.