# Question regarding vectors.

#### sankalpmittal

1. Homework Statement

The x and y components of vector P have numerical values 6 and 6 , respectively , and that of P + Q have numerical values 10 and 9. What are the numerical values of x and y components of vector Q ?

Note this problem gave the following values :

|Px| = 6
|Py|=6
|P + Q| = 10 or 9
|Qx| = ? To find..
|Qy|=? To find...

2. Homework Equations

|P + Q|2 = P2 + Q2
+2PQcosθ

Here |P| = P
|Q| = Q

3. The Attempt at a Solution

( Px = Py = 6)

P2 = Px2 + Py2
P2 = 72
P = 6√2

|P + Q|2 = P2 + Q2
+2PQcosθ

Putting P= 6√2
and

|P + Q| = 10 (given)

and also |P + Q| = 9 (given)

I get two equations :

Q2 + 12√2 Qcosθ = 28
Q2 + 12√2 Qcosθ = 9

Now what ??? How will I proceed ?

Thanks in advance...

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#### Infinitum

Hi sankalpmittal

Why use such a long approach?? You can simply see that P vector is given as, $\vec{P}=6i + 6j$ and $\vec{P}+\vec{Q}= 10i + 9j$, where i, j are unit vectors in the respective directions...So what would vector Q be?

#### sankalpmittal

Hi sankalpmittal

Why use such a long approach?? You can simply see that P vector is given as, $\vec{P}=6i + 6j$ and $\vec{P}+\vec{Q}= 10i + 9j$, where i, j are unit vectors in the respective directions...So what would vector Q be?
The magnitude of x and y components of Q vector will be 4,3 !! That's what the answer given in the question booklet !!

Thanks Infinitum !!

Moral : Keep things simple..

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