# Vectors [Solved!]

**Swalay** 05 Sep 2016, 06:25

### My question

In the diagram

AB = p

CA = q

and DC = 4 AB

E is the point such that BE = kq

d) Given that D, A and E lie on a straight line find the value of k.????

### Relevant page

3. Vectors in 2 Dimensions

### What I've done so far

Answers so far:

a) DC+CA=DA

Hence DA = 4p + q

b) Again CB = CA+AB

Hence CB = q + p

c) Again AE = AB + BE

Therefore AE= p + kq

X

<img src="/forum/uploads/imf-triangle.jpg" width="427" height="340" alt="vectors" />
In the diagram
AB = p
CA = q
and DC = 4 AB
E is the point such that BE = kq
d) Given that D, A and E lie on a straight line find the value of k.????

Relevant page
<a href="/vectors/3-vectors-2-dimensions.php">3. Vectors in 2 Dimensions</a>
What I've done so far
Answers so far:
a) DC+CA=DA
Hence DA = 4p + q
b) Again CB = CA+AB
Hence CB = q + p
c) Again AE = AB + BE
Therefore AE= p + kq

## Re: Vectors

**Murray** 05 Sep 2016, 22:18

@Swalay: What can you tell me about the lines AB and DC?

How about the lines CA and BE?

What can we conclude about the 2 triangles ?DCA and ?ABE?

X

@Swalay: What can you tell me about the lines AB and DC?
How about the lines CA and BE?
What can we conclude about the 2 triangles ?DCA and ?ABE?

## Re: Vectors

**Swalay** 06 Sep 2016, 04:49

AB and DC are parallel

CA and BE are parallel

Triangles DCA and ABE are congruents

Thank you for your help so far

AB/BE=DA/CA

(P+kq)/kq = (4p+q)/q

k=1/4

X

AB and DC are parallel
CA and BE are parallel
Triangles DCA and ABE are congruents
Thank you for your help so far
AB/BE=DA/CA
(P+kq)/kq = (4p+q)/q
k=1/4

## Re: Vectors

**Murray** 06 Sep 2016, 04:54

Actually, the triangles aren't **congruent** (which means same size, same shape), but **similar** (same shape, different size).

Your final answer is correct!

X

Actually, the triangles aren't <b>congruent</b> (which means same size, same shape), but <b>similar</b> (same shape, different size).
Your final answer is correct!

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