# How can I calculate the magnitude of vectors?

The following procedures can be used to calculate a vector's magnitude:

Now, draw the two vectors' horizontal and vertical components to create a vector triangle that has a right angle triangle formed in its center.

Find the unknown quantity now by applying the Pythagorean theorem.

Magnitude is just the two provided vectors' modulus put simply.

that is, root over (a^2+b^2).

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To calculate the magnitude of a vector, use the formula:

[ \text{Magnitude} (|\mathbf{v}|) = \sqrt{v_1^2 + v_2^2 + \ldots + v_n^2} ]

Where ( \mathbf{v} ) is the vector with components ( v_1, v_2, \ldots, v_n ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Objects A and B are at the origin. If object A moves to #(5 ,-1 )# and object B moves to #(-7 ,2 )# over #3 s#, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.
- A projectile is shot from the ground at an angle of #(5 pi)/12 # and a speed of #3/5 m/s#. Factoring in both horizontal and vertical movement, what will the projectile's distance from the starting point be when it reaches its maximum height?
- What is the projection of #<-5,3,7 ># onto #<0,8,-2 >#?
- What is the projection of #<6,5,3 ># onto #<2,-1,8 >#?
- What is the dot product of #<8,4,1># and #<4,-2,3 >#?

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