What Are the Components of Vector Q?

[sankalpmittal]

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 :

|P^→_x| = 6
|P^→_y|=6
|P^→ + Q^→| = 10 or 9
|Q^→_x| = ? To find..
|Q^→_y|=? To find...

Homework Equations

|P^→ + Q^→|² = P² + Q²
+2PQcosθ

Here |P^→| = P
|Q^→| = Q

The Attempt at a Solution

( P_x = P_y = 6)

P² = P_x² + P_y²
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...

 

[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..

 

[Infinitum]

Moral : Keep things simple..

Well, usually