Finding unknown given vector a,b and parallel

Vectors are crucial in many areas of mathematics, physics, engineering and computer science. They can be used to represent and manipulate quantities that have both magnitude and direction, such as velocity, force, acceleration, and electric and magnetic fields. They also have many practical applications, such as in navigation, computer graphics and animation, and robotics. So while vectors may seem confusing at first, they are an important tool in many fields and worth taking the time to understand.
  • #1
xplosiv3s
13
0

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!
 
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  • #2
xplosiv3s said:

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.
xplosiv3s said:
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!
 
  • #3
Mark44 said:
nonzero scalar multiple of the other.

So i multiply the other side by 3 because it has to be that? ^
 
  • #4
xplosiv3s said:
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.
 
  • #5
Dick said:
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 >.>
 
  • #6
I can understand why everyone hates vectors
 
  • #7
xplosiv3s said:
I can understand why everyone hates vectors
Vectors are marvelous !
 

FAQ: Finding unknown given vector a,b and parallel

1. What is the process for finding an unknown vector given two parallel vectors, a and b?

The process for finding an unknown vector given two parallel vectors, a and b, is to use the properties of parallel vectors. This means that the unknown vector will have the same direction and magnitude as the given parallel vectors. You can find the direction and magnitude of the unknown vector by using the components of the given parallel vectors.

2. How do I determine the direction of the unknown vector using the given parallel vectors?

To determine the direction of the unknown vector, you can use the direction of the given parallel vectors. If the given vectors are pointing in the same direction, the unknown vector will also point in that direction. If the given vectors are pointing in opposite directions, the unknown vector will point in the opposite direction.

3. Can I find the magnitude of the unknown vector using the given parallel vectors?

Yes, you can find the magnitude of the unknown vector by using the magnitude of the given parallel vectors. The magnitude of the unknown vector will be equal to the magnitude of either of the given vectors.

4. Is there a specific formula for finding an unknown vector given two parallel vectors?

Yes, there is a specific formula for finding an unknown vector given two parallel vectors. It is given by:
Unknown vector = (Magnitude of given vector / Magnitude of parallel vector) * Parallel vector

5. Can I use this method to find an unknown vector if the given vectors are not parallel?

No, this method can only be used to find an unknown vector if the given vectors are parallel. If the given vectors are not parallel, then you will need to use a different method, such as the cross product or the dot product, to find the unknown vector.

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