# Thread: Vector of P magnitude: O(0,0), A(-1,3), B(-5,4), C(7,P)

1. ## Vector of P magnitude: O(0,0), A(-1,3), B(-5,4), C(7,P)

Hello, I have four points O (0,0) A(-1,3) B(-5,4) and C(7,P)

I have found vector AC to be (8, (p-3))

Now the question is stating what are the values of P for which '' l Vector AC l '' (those two vertical lines are included)=10

Im guessing this is th magnitude so I sub it into the formula which would be (sqrt) (82+(p-3)2)= 10

But from here I keep failing and I am not sure what to do, because I keep ending up with (sqrt) (64 + (p-3)2) =10
And if I try to solve (p-3)2 = 0 to get values for P I would end up with P=3 and then my answer for the equation would just not give me the correct answer.

How do i solve this?

2. Originally Posted by richiesmasher
And if I try to solve (p-3)2 = 0
Could you clarify where this came from?

3. Originally Posted by lev888
Could you clarify where this came from?
It didnt come from anywhere, I just figured to solve the overall equation I could solve that equation separately first.

SO I know (p-3)2 is a perfect square

So: (p-3) (p-3) =0

Each value of p would be then 3

So I used that in the equation i guess?

4. Originally Posted by richiesmasher

SO I know (p-3)2 is a perfect square

So: (p-3) (p-3) =0
Yes, I was asking how you figured out that the next step would be that equation. I don't quite understand the reasoning. First, I don't see any requirements that (p-3)2 should be a perfect square. And even if it is, why 0?

5. Originally Posted by lev888
Yes, I was asking how you figured out that the next step would be that equation. I don't quite understand the reasoning. First, I don't see any requirements that (p-3)2 should be a perfect square. And even if it is, why 0?
Idk because it's a quadratic?

6. Originally Posted by richiesmasher
Idk because it's a quadratic?
Just try to solve sqrt(82+(p-3)2) = 10 without any assumptions. Hint: sqrt(x) = 10. What is x?

7. Originally Posted by lev888
Just try to solve sqrt(82+(p-3)2) = 10 without any assumptions. Hint: sqrt(x) = 10. What is x?
x = (82+(p-3)2)

So therefore this

(82+(p-3)2)= 100

Am I on to something?

8. Originally Posted by richiesmasher

Am I on to something?

Looks good, keep going.

9. Originally Posted by lev888
Looks good, keep going.
(82+(p-3)2)=100
64+p2-6p+9=100

p2-6p-27=0

p2+3p-9p-27=0

p(p+3)-9(p+3)

Therefore :

(p+3) (p-9)=0

p = 9 and p=-3

10. Check the last step.

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