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## Precalculus (2018 edition)

### Unit 3: Lesson 2

Magnitude of vectors

# Vector magnitude from components

Sal finds the magnitude of a vector given its components of (5, -3).

## Want to join the conversation?

• So wait, do we always have to assume a vector starts at (0,0) if ve are only given one of its components? (In this case a)
• No. It is convenient to draw vectors starting at the origin, but it is NOT necessary.

5 is just the vector's LENGTH, and -3 is just the vector's HEIGHT. You can draw the vector starting at any point on the graph, but you have to make sure it has a length of 5 and a height of negative 3.

For example: If you drew the vector starting at point (1, 1) then its terminal point would be (6, -2)
• Why does Sal use two bars to indicate magnitude (||a||) instead of one (|a|)? Is there a reason for that or can either way be used interchangeably?
• The convention is to use double bars for vectors and single bars for complex numbers and scalars.
• Can the magnitude of a vector formed by irrational scalars be negative?
• My understanding of MAGNITUDE is that it is the length of the vector and therefore cannot be negative. But its DIRECTION can be positive or negative.
• Why is the magnitude of a vector denoted as ||x|| rather than |x|?
• Why does Sal use the `distance` formula to find the `magnitude` of the vector?
(1 vote)
• Because the magnitude is the length of the vector. In other words, it's the distance between 2 points.
• isn't the proper way to denote a vector something like: <1,1> and not (1,1)? I've always seen vectors with <> but maybe that's only for unit vectors?
• I've never seen the <x,y> notation however, I have seen the (x,y) row vector or column vector notation (two big brackets with the x on top and y on bottom inside the brackets). The row vector/column vector notation will be used in matrix algebra.
(1 vote)
• my teacher always draws the vectors with pointy parentheses. Is there a reason why? They are called angle brackets.
(1 vote)
• This is a notational norm. Since you could potentially confuse (x,y) with a coordinate point, using <x,y> simply tells you, "this is a vector" so you just know when you see the brackets.
• If I have a vector's magnitude, and it's heading (angle) then how do I calculate the components?
(1 vote)
• The short version is.
Given a vector with v with the magnitude r and direction θ. The x component is r•cos(θ) and the y component is r•sin(θ)