Finding unknown given vector a,b and parallel

[xplosiv3s]

Homework Statement

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

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

Homework Equations

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


Additional information:
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!

 

[Mark44]

Homework Statement

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

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

Homework Equations

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)

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.

giving μ = 7/9

However μ = -1


Additional information:
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!

 

[xplosiv3s]

nonzero scalar multiple of the other.

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

 

[Dick]

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

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.

 

[xplosiv3s]

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.

Ok thanks! That kinda makes sense!

actually nvm >.>

 

[xplosiv3s]

I can understand why everyone hates vectors

 

[SammyS]

I can understand why everyone hates vectors

Vectors are marvelous !