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# C4 practice paper vector question watch

1. How should part (c) be done? I found the line connecting A and B, and then equated it to P to find lambda at P, but I'm not sure if this is right.

Appreciate your help, thanks
2. (Original post by ezioaudi77)

How should part (c) be done? I found the line connecting A and B, and then equated it to P to find lambda at P, but I'm not sure if this is right.

Appreciate your help, thanks
The "point P" is actually the equation of a straight line in disguise...

if you rearrange it, as in the mark scheme, (and let r denote the straight line) it becomes

so if you try and imagine it, the question is to actually try and show the points A and B lie on the line r (i.e. show that the points A and B the position vector -9k plus some some scale factor of the direction vector of lambda)
3. (Original post by boner in jeans)
x
When I see "point P", I would never think of it as a vector equation of a line. But your explanation makes sense, thanks
4. I have a vector question if anyone can help please,
The coordinates of points A,B and C are (4,2,-5), (10,2,-7) and (12,5,9)
a) find a vector equation of the line l1 that passes through A and B
I did this and got r=4i + 2j - 5k +lambda(6i + 2k) which is correct

b) Point X is on l1 such that direction vector CX is perpendicular to AB, find the coordinates of X.

This is what I'm stuck on, help please!!
5. (Original post by JenniS)
I have a vector question if anyone can help please,
The coordinates of points A,B and C are (4,2,-5), (10,2,-7) and (12,5,9)
a) find a vector equation of the line l1 that passes through A and B
I did this and got r=4i + 2j - 5k +lambda(6i + 2k) which is correct

b) Point X is on l1 such that direction vector CX is perpendicular to AB, find the coordinates of X.

This is what I'm stuck on, help please!!
OX can be written as (4 +6λ)i + (2)j + (-2 -5λ)k.

CX = OX - OC.

If you know the dot product rule, you can find λ by CX∙AB=0.

Substitute the value you found for λ in (4 +6λ)i + (2)j + (-2 -5λ)k, and you can find the coordinates of X

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