# Vectors [Pending...]

**asad** 07 Oct 2016, 07:45

### My question

In the figure (also at http://prnt.sc/cqth0m), vector OB is three times longer than OA, BC is parallel to OA and twice its length. CD is parallel to BA.

Angle AOB = 60 degrees. If A and B have position vectors a and b respectively relative to O; and CD = kBA, find:

a) vector expression for BA and OD

b) find k if OD is perpendicular to AB

### Relevant page

Vectors

### What I've done so far

(a) BA = BO + OA = -b + a = a-b

Now how to find OD?

Since OB = 3OA, does this mean b=3a? And what is use of this information?

BC=2OA

CD=pBA

OD= OB+BC+CD = b+2a+p(a-b),which is not correct I know

For (b),AB would be =b-a, and OD would be found from (a), but what happens if it is perpendicular?

X

<img src="/forum/uploads/imf-3239-ques.png" width="500" height="313" alt="vectors" />
In the figure (also at <a href="http://prnt.sc/cqth0m">http://prnt.sc/cqth0m</a>), vector OB is three times longer than OA, BC is parallel to OA and twice its length. CD is parallel to BA.
Angle AOB = 60 degrees. If A and B have position vectors a and b respectively relative to O; and CD = kBA, find:
a) vector expression for BA and OD
b) find k if OD is perpendicular to AB

Relevant page
<a href="http://www.intmath.com/forum/vectors-39/vectors:108">Vectors</a>
What I've done so far
(a) BA = BO + OA = -b + a = a-b
Now how to find OD?
Since OB = 3OA, does this mean b=3a? And what is use of this information?
BC=2OA
CD=pBA
OD= OB+BC+CD = b+2a+p(a-b),which is not correct I know
For (b),AB would be =b-a, and OD would be found from (a), but what happens if it is perpendicular?

## Re: Vectors

**Murray** 08 Oct 2016, 23:37

Hi Asad

As some general hints for this kind of question, it's good to separate the **vector** diagram (where you use vector addition and subtraction, as you've done in the first part of your answer), and the related **scalar** diagram, where you just deal with the lengths involved.

(Just a small point - your question has `k` as the unknown variable, and then you have used `p` in your answer. Let's stick to `k`.)

It's not so easy to see what's going on in the given diagram (that's probably deliberate on the part of the question writers).

Here's the vector diagram, this time drawn to scale (I've used GeoGebra to draw the diagram):

You wrote:

(a) **BA = BO + OA = -b + a = a-b**

Yes, OK.

Now how to find **OD**?

Since **OB** = 3 **OA**, does this mean **b = 3a**?

Actually, no. This is what I meant about separating out the vector and scalar diagrams. Vector **b** is 3 times longer than vector **a**, but they are pointing in different directions, so we can't say **b = 3a**.

And what is use of this information?

We'll use it in the scalar diagram.

**BC** = 2**OA**

**CD** = `k`**BA**

**OD = OB + BC + CD = b + **2**a** + `k`**(a-b)**, which is not correct I know

Actually, I think it is correct (with the `p` changed back to `k`)!

For (b), **AB**? would be **=b-a**, and **OD** would be found from (a), but what happens if it is perpendicular?

Before going on to this, can you draw a scalar diagram now, showing the known lengths? It will help a lot, I think.

X

Hi Asad
As some general hints for this kind of question, it's good to separate the <b>vector</b> diagram (where you use vector addition and subtraction, as you've done in the first part of your answer), and the related <b>scalar</b> diagram, where you just deal with the lengths involved.
(Just a small point - your question has `k` as the unknown variable, and then you have used `p` in your answer. Let's stick to `k`.)
It's not so easy to see what's going on in the given diagram (that's probably deliberate on the part of the question writers).
Here's the vector diagram, this time drawn to scale (I've used GeoGebra to draw the diagram):
<img src="/forum/uploads/imf-2519-vector-diagram.png" width="360" height="307" alt="Vectors" />
You wrote:
<blockquote>(a) <b>BA = BO + OA = -b + a = a-b</b></blockquote>
Yes, OK.
<blockquote>Now how to find <b>OD</b>?
Since <b>OB</b> = 3 <b>OA</b>, does this mean <b>b = 3a</b>?</blockquote>
Actually, no. This is what I meant about separating out the vector and scalar diagrams. Vector <b>b</b> is 3 times longer than vector <b>a</b>, but they are pointing in different directions, so we can't say <b>b = 3a</b>.
<blockquote>And what is use of this information?</blockquote>
We'll use it in the scalar diagram.
<blockquote><b>BC</b> = 2<b>OA</b>
<b>CD</b> = `k`<b>BA</b>
<b>OD = OB + BC + CD = b + </b>2<b>a</b> + `k`<b>(a-b)</b>, which is not correct I know</blockquote>
Actually, I think it is correct (with the `p` changed back to `k`)!
<blockquote>For (b), <b>AB</b>? would be <b>=b-a</b>, and <b>OD</b> would be found from (a), but what happens if it is perpendicular?</blockquote>
Before going on to this, can you draw a scalar diagram now, showing the known lengths? It will help a lot, I think.

## Re: Vectors

**Murray** 26 Oct 2016, 23:39

It seems Asad has disappeared. Anyone else like to have a go at finishing it?

X

It seems Asad has disappeared. Anyone else like to have a go at finishing it?

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