1. ## Vector..

Given that a=3i-2j, b=3i+j and c=-6i+j, express pa-qb in terms of p,q,i and j. Hence, find the value of p and of q if pa-qb is equal to the unit vector along the straight line 4x+3y=12

2. ## Re: Vector..

Originally Posted by Trefoil2727
Given that a=3i-2j, b=3i+j and c=-6i+j, express pa-qb in terms of p,q,i and j. Hence, find the value of p and of q if pa-qb is equal to the unit vector along the straight line 4x+3y=12
Do you intend to show any of your own work?

3. ## Re: Vector..

well, I have to admit that I don't know how to solve it..

4. ## Re: Vector..

Trefoil it is simple...
what pa means?
what qb means?

multiplicationnnnn..........so as Plato suggests........ just do itttttttttttttttttttttt .

5. ## Re: Vector..

You are told exactly what to do: you are given pa+ qb and you are told that a= 3i-2j, b=3i+j. It's just integer arithmetic.

6. ## Re: Vector..

this interesting

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7. ## Re: Vector..

Really good one question and i don't solve this question and if you know the answer just share with me.

8. ## Re: Vector..

Given that a=3i-2j, b=3i+j and c=-6i+j, express pa-qb in terms of p,q,i and j. Hence, find the value of p and of q if pa-qb is equal to the unit vector along the straight line 4x+3y=12
Since it has been a while: It is, as I said, integer arithmetic. pa= p(3i- 2j)= 3pi- 2pj. qb= q(3i+ j)= 3qi+ qj. pa- qb= 3pi- 2pj- (3qi+ qj)= (3p- 3q)i-(2p+ q)j.

A vector pointing along the straight line 4x+ 3y= 12 is 4i+ 3j which has length $\sqrt{4^2+ 3^2}= 5$ so a unit vector in that direction is (4/5)i+ (3/5)j

We have (3p- 3q)i- (2p+ q)j= (4/5)i+ (3/5)j so solve 3p- 3q= 4/5 and -2p- q= 3/5 for p and q.