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a level vectors question

idk how to do this question
https://imgur.com/a/MvA5ejO
for part a its the vector equation of the line (x, y, z) + lambda*(i,j,k) where (x,y,z) is the starting position vector and (i,j,k) is the direction vector and lambda is a scalar.

so say A is the starting position vector then the equation of the line is
(4, -3, 5) + lambda*(i,j,k)
(i,j,k) can be found by working out the vector needed for A->B

you know this line goes through C
then you basically have three equations as you know that all of them must satisfy the coords of point C.
So then you can work out lambda and then p.
(edited 8 months ago)
Reply 2
Original post by esha06
idk how to do this question
https://imgur.com/a/MvA5ejO

1) I think the following is simpler:

->AB = k(->BC) (-> means the vector)

plug in values given and work out k

2) This is not easy,

We can create 2 equations for ->CD,

->CD = n(->OA) (because CD and OA are parallel, so one is a fraction of the other)

->CD = ->(CO) + z(->OB) (because OB has been extended by some value z)

Set these two equations equal to each other, and create some simultaneous equations for the i,j and k components

Let me know if still unsure

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