If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Get ready for AP® Calculus>Unit 8

Lesson 4: 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.
• Are we assuming that the ray a starts from the origin (0, 0)?
• Depends on the context of the question. In our case yes it started at (0,0) but always pay attention to the change in x and y of the vector because vectors can be position anywhere and still have the same magnitude.

Also the vector wouldn't be considered a ray since the vector's length doesn't start at one point then infinitely goes to another.
(I know this question is old this is more for me to get myself to express what I learned)
• Why is the magnitude of a vector denoted as ||x|| rather than |x|?
• To some people using 1 pair of brackets can mean absolute value.
(1 vote)
• 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.