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# vector question watch

1. question 4 part c...

here was my method:

i made 3 equations by equating each of the i, j, k components of OP and AB

then i did some fairly basic manipulation to show that the three equations are identical

and so they will all always be satisfied so the point P must lie on AB

I also have no idea what they mean by 'find the foot' in part e, although it's fairly clear what they've done in the mark scheme; just substituted lambda=2 into OP, i just don't see why...
Attached Files
2. C4 Practice Paper A3 mark scheme.doc (124.5 KB, 59 views)
3. C4 Practice Paper A3.doc (61.0 KB, 114 views)
4. (Original post by TPJY)
question 4 part c...

here was my method:

i made 3 equations by equating each of the i, j, k components of OP and AB

then i did some fairly basic manipulation to show that the three equations are identical

and so they will all always be satisfied so the point P must lie on AB

I also have no idea what they mean by 'find the foot' in part e, although it's fairly clear what they've done in the mark scheme; just substituted lambda=2 into OP, i just don't see why...
For (c), it's perfectly acceptable to let the line through A and B have the equation

and construct three identical equations, as you did.

For (e), draw a sketch and think.What do you normally associate the word 'foot' with?
5. (Original post by TPJY)
question 4 part c...

here was my method:

i made 3 equations by equating each of the i, j, k components of OP and AB

then i did some fairly basic manipulation to show that the three equations are identical

and so they will all always be satisfied so the point P must lie on AB

I also have no idea what they mean by 'find the foot' in part e, although it's fairly clear what they've done in the mark scheme; just substituted lambda=2 into OP, i just don't see why...
For 4c
The given line is passing through A and B
1. You should to examine wether A and B is on the given line
This means to give such that the equation
gives the coordinates of point A and B respectively
For A and for B as
is written in the answer scheme.
2. For line passing through a point with direction vector AB

where is point A on the line and

so the line

Now arranging the given equation

This is same as the equation of line given by us with that

For e)
The 'foot' is the point where the perpendicular OP meets the line passing
through AB, that is the point P. For P the lambda is calculated in D

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