- #1

- 785

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## 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}= P

^{2}+ Q

^{2 }+2PQcosθ

Here |P

^{→}| = P

|Q

^{→}| = Q

## The Attempt at a Solution

( P

_{x}= P

_{y}= 6)

P

^{2}= P

_{x}

^{2}+ P

_{y}

^{2}

P

^{2}= 72

P = 6√2

|P

^{→}+ Q

^{→}|

^{2}= P

^{2}+ Q

^{2 }+2PQcosθ

Putting P= 6√2

and

|P

^{→}+ Q

^{→}| = 10 (given)

and also |P

^{→}+ Q

^{→}| = 9 (given)

I get two equations :

Q

^{2}+ 12√2 Qcosθ = 28

Q

^{2}+ 12√2 Qcosθ = 9

Now what ??? How will I proceed ?

Thanks in advance...