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## Precalculus (2018 edition)

### Unit 3: Lesson 2

Magnitude of vectors

# Vector magnitude from initial & terminal points

Example of finding the magnitude of a vector when what we're given about the vector is where it starts and where it ends.

## Want to join the conversation?

• If Vector u is on the x-axis and Vector a is on the y-axis, Vector u doesn't have any components along the y-axis, correct?
• That is correct. However, you could also say that vector u has a y-component of 0.
• Can you find the magnitude of a sum of two magnitudes
• I assume you are asking about finding the magnitude of two vectors added by adding them together? That only works if they are pointed in the exact same direction. Otherwise you have to do vector addition and find the composite net magnitude.
• What are vectors specifically used for in math? Sal just introduces us to the components of vectors but never specifies why and how we use them.
• Vectors are used frequently in physics to describe things such as forces, velocity, and acceleration. We can use vector fields to describe gravity, electric fields, fluid flow, and more.
• Isn't it possible to find the magnitude of a similar vector without drawing?
• Sure
1. calculate distance between points
2. use distance formula
(good thing about vectors is, that the
magnitude is a scalar, and it won't matter
if you switch starting and endpoint)
(1 vote)
• What if the magnitude is given and 1 pair of points and youre asked to find the other pair, how will you do that?
• There must be a direction as well, or its not a vector quantity.
Let magnitude = r, and let direction = Θ. Find the x component with r·cosΘ, and the y component with r·sinΘ. Finally, add that result to the start point, x₂+x₁ , and y₂+y₁ to find the end point.
• if we can find magnitude this way then why are unit vectors used in vector calculations too ?
(1 vote)
• We use unit vectors when we want to discuss direction only, and not magnitude. For example, the formula for gravitational force between two objects is (GmM/d²)·r , where r is a unit vector along the line between the two objects. This way, different values of m, M (the objects masses) and d (the distance between them) are the only things that affect the magnitude of the force.
• why do we write ||w||=(9,-4) instead of ||w||=(0,0)(9,-4)? This would make writing terminal vectors easier?
E.g ||w||=(-7,3)(2,-1)
• Vectors don't have a location, only direction and magnitude. The vector (9,4) could have a start point at (0,0) or (3,0) or anywhere. Think of the wind,it is a vector, it comes from a direction and it has a velocity but we don't talk about it as "starting at location Latitude a or Longitude b".
(1 vote)
• could you use the distance formula
• The magnitude formula is literally just the distance formula with change, so yes, pretty much.
(1 vote)
• What does Mr. Khan mean when he says, "And so, for example, in this situation, you could actually define our vector w by the sum of two vectors"?
• This is actually basic vector addition. You add the x and y components to get the final vector w.
(1 vote)
• How can you differentiate two numbers being used as coordinates and the two numbers specifying the x and y components?

ex: vector v = (-3,1). This point is the terminal point.
vector w = (9,-4). This has the x and y components.