New Maths 9-1 GCSE Exam Style Question HELP NEEDED!!?

Can anyone give me a little clue on how to do question b)???
I worked out vector AQX to be -4a+12b but then how do i prove that to be a straight line??

(edited 7 years ago)

Reply 1

Oooshiebaby

7

Ah, I was doing this just before Christmas.
With vectors, for 2 lines to be on the same line, they must share 2 things: A common point and the same gradient. Hope this info helps, gimme a few minutes and I'll work it out myself and can therefore help you further.

Reply 2

NothingButWaleed

OP

14

Original post by RamonDavis

Ah, I was doing this just before Christmas.
With vectors, for 2 lines to be on the same line, they must share 2 things: A common point and the same gradient. Hope this info helps, gimme a few minutes and I'll work it out myself and can therefore help you further.

ok

Reply 3

Oooshiebaby

7

I've worked it out :smile:

Firstly, to Prove it is a straight line you basically need to prove that the middle point, Q, is on the line.
So here is a question for you, what 2 lines could you use to show Q is going in the same direction as X?

Reply 4

NothingButWaleed

OP

14

Original post by RamonDavis

I've worked it out :smile:

Firstly, to Prove it is a straight line you basically need to prove that the middle point, Q, is on the line.
So here is a question for you, what 2 lines could you use to show Q is going in the same direction as X?

I don't understand....

Reply 5

Oooshiebaby

7

Hmm ok.
You should have A to Q as 3b-a from the last question.
So this means that if A to X has the same gradient, it must be on the same line as they share the common point of A.
So you need to work out A to X

Reply 6

Darth_Narwhale

8

Yeah Ramon is right. Find the vector for AQ, and then for AX. You'll find that AX is a multiple of AQ. This means that they have the same direction (or gradient), but different magnitudes (lengths). In other words, AX is parallel to AQ. However because they both go through the same point, A, the must be the same line.

Reply 7

Notnek

21

Original post by NothingButWaleed

I don't understand....

To prove that three points A, B and C are in a straight line using vectors, you need to show that any two of the vectors that make up the line are parallel.

E.g. you could show that

\vec{AB}

is parallel to

\vec{AC}

or you could show that

\vec{AB}

is parallel to

\vec{BC}

etc.

Reply 8

NothingButWaleed

OP

14

Original post by Darth_Narwhale

Yeah Ramon is right. Find the vector for AQ, and then for AX. You'll find that AX is a multiple of AQ. This means that they have the same direction (or gradient), but different magnitudes (lengths). In other words, AX is parallel to AQ. However because they both go through the same point, A, the must be the same line.