# Finding unknown given vector a,b and parallel

1. Feb 16, 2012

### xplosiv3s

1. The problem statement, all variables and given/known data

Given that c= 3i + 4j and d= i - 2j

find μ when μc + d is parallel to i +3j

2. Relevant equations

3. The attempt at a solution

3iμ + 4jμ + i + j

i( 3μ + 1) + (4μ -2) j

since it is parallel to i + 3j therefore 3μ+1=3(4μ-2)

giving μ = 7/9

However μ = -1

Apparently (see bold) I am supposed to multiply the LHS by 3 instead of the RHS but by equating I and J vectors and looking at the parallel line it would seem logical to do it the way I have (or am I being retarded?). I can accept that I have the multiply LHS instead of RHS but I don't understand why!!

2. Feb 16, 2012

### Staff: Mentor

Not necessarily. Vectors can be parallel without being equal. Two vectors are parallel if either of them is some nonzero scalar multiple of the other.

3. Feb 16, 2012

### xplosiv3s

So i multiply the other side by 3 because it has to be that? ^

4. Feb 16, 2012

### Dick

If a vector is parallel to i+3j, then 3 times the i component is equal to the j component. Since 3*1=3. So 3*(3μ+1)=(4μ-2). I'm not sure why you are doing it the other way around.

5. Feb 16, 2012

### xplosiv3s

Ok thanks! That kinda makes sense!

actually nvm >.>

6. Feb 16, 2012

### xplosiv3s

I can understand why everyone hates vectors

7. Feb 16, 2012

### SammyS

Staff Emeritus
Vectors are marvelous !!!