Find values of a making one vector parallel to the other

In summary, making one vector parallel to the other means finding a value (a) that results in both vectors having the same direction but possibly different magnitudes. This allows for easy manipulation and comparison of vectors. The values of a can be found using the scalar multiple property of vectors, and there can be an infinite number of values that make two vectors parallel. If the two vectors are already parallel, there is no need to find additional values of a.
  • #1
loganblacke
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Find values of "a" making one vector parallel to the other

Homework Statement



Find the value(s) of a making vector v = 4ai - 2j, parallel to vector w = a^2i +4j

Homework Equations


P= (a dot b/ magnitude b^2) (bi, bj)


The Attempt at a Solution


I can plug and chug, but at what point do you solve for a?
 
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  • #2


If you can find a vector that's perpendicular to v, then you can just plug and chug on finding when u.w=0.
 

FAQ: Find values of a making one vector parallel to the other

1. What does it mean to make one vector parallel to the other?

Making one vector parallel to the other means to find a value (a) that will result in both vectors having the same direction, but possibly different magnitudes. This essentially means that the two vectors will be pointing in the same direction, even if one is longer or shorter than the other.

2. Why is it important to find values of a that make one vector parallel to the other?

Finding values of a that make one vector parallel to the other is important because it allows us to manipulate and compare vectors in a meaningful way. By making two vectors parallel, we can easily determine if they are equal or if one is a scalar multiple of the other.

3. How do you find values of a that make one vector parallel to the other?

To find values of a that make one vector parallel to the other, we can use the scalar multiple property of vectors. This states that if we multiply a vector by a scalar, the resulting vector will be parallel to the original. Therefore, we can find the scalar multiple (a) by dividing the components of one vector by the corresponding components of the other vector.

4. Can there be more than one value of a that makes one vector parallel to the other?

Yes, there can be more than one value of a that makes one vector parallel to the other. This is because there are an infinite number of scalar multiples that can result in a parallel vector. As long as the direction of the two vectors are the same, they can be considered parallel.

5. What if the two vectors are already parallel, do we still need to find values of a?

If the two vectors are already parallel, then they will have the same direction and therefore, will not require any additional values of a to make them parallel. In this case, the value of a would simply be the scalar multiple that already exists between the two vectors.

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