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[SOLVED] C4 - Vectors (As Per Usual)

Vectors are definitely my weakest subject in A-Level Maths, I find the first few parts of questions relatively easy but the final part always baffles me :-(

Thanks again for all your help!
Conor

The point D is the point on the line p which is closest to the origin O
Find the coordinates of D.

I know the coordinates of points A, B and C on the line, how would I go about finding D?

(edited 10 years ago)

Reply 1

Solivagant

Original post by InfernoxCJC

Vectors are definitely my weakest subject in A-Level Maths, I find the first few parts of questions relatively easy but the final part always baffles me :-(

Thanks again for all your help!
Conor

The point D is the point on the line p which is closest to the origin O
Find the coordinates of D.

I know the coordinates of points A, B and C on the line, how would I go about finding D?

I see you are struggling to find the D... :colone:

Back to the maths, what have you tried so far?

Reply 2

maggiehodgson

Original post by InfernoxCJC

Vectors are definitely my weakest subject in A-Level Maths, I find the first few parts of questions relatively easy but the final part always baffles me :-(

Thanks again for all your help!
Conor

The point D is the point on the line p which is closest to the origin O
Find the coordinates of D.

I know the coordinates of points A, B and C on the line, how would I go about finding D?

I struggle with vectors too. I have found, sometimes, that making a diagram helps me to see what's needed. It doesn't matter where you put the co-ordinates but label them. It also helps to put in the origin. Again, anywhere seems to be OK.

Hope it works for you.

Reply 3

InfernoxCJC

Original post by CJG21

I see you are struggling to find the D... :colone:

Back to the maths, what have you tried so far?

Thanks for your reply,
that is my problem. I have no idea.
As I said I have the cooridinates of points A B and C on the line and am told D is the point on the line closest to O but, unless I am missing something obvious I don't have any other information and as far as I can tell I need something else?

The points A and B have coordinates (3, 9, -7) and (13, -6, -2) respectively.

a) Find, in vector form, an equation for the line p which passes through A and B.
b) Show that the point C with coordinates (9, 0, -4) lies on p

The point D is the point on p closest to the origin O.
c) Find D

(edited 10 years ago)

Reply 4

SherlockHolmes

Original post by InfernoxCJC

If point D is the point on p closest to the origin O, then the direction of the line OD will be perpendicular to the line p. Perhaps you could use the scalar product to show this?

Reply 5

InfernoxCJC

Original post by SherlockHolmes

If point D is the point on p closest to the origin O, then the direction of the line OD will be perpendicular to the line p. Perhaps you could use the scalar product to show this?

How can you be 100% sure D is perpendicular though? I had a feeling this was the solution but, what if the lines was something like this

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D

.........................0

In this situation, vector OD would not be perpendicular to the line p

Reply 6

TSR561

Original post by InfernoxCJC

How can you be 100% sure D is perpendicular though? I had a feeling this was the solution but, what if the lines was something like this

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D

.........................0

In this situation, vector OD would not be perpendicular to the line p

You know D is on the line P, and that it is also the shortest distance to O. It therefore follows that OD is perpendicular to the line. Think about it, can you get any shorter than a direct line towards P?