# What is # || < 4 , 9 , -8 > || #?

The two vertical lines just mean 'the length of' the vector:

It probably doesn't need much more explanation, but it's important to be aware of the formula for determining a vector's length because it's a useful tool.

It is likely important to note that even though this is a three-dimensional vector, it is still a square root and not a cube root.

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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.

- A projectile is shot from the ground at an angle of #pi/6 # and a speed of #3 m/s#. When the projectile is at its maximum height, what will its distance, factoring in height and horizontal distance, from the starting point be?
- Objects A and B are at the origin. If object A moves to #(-2 ,8 )# and object B moves to #(3 ,-3 )# over #4 s#, what is the relative velocity of object B from the perspective of object A?
- A projectile is shot at a velocity of # 12 m/s# and an angle of #pi/6 #. What is the projectile's peak height?
- What is the projection of #<2,-5,1 ># onto #<6,-8,3 >#?
- A bird is flying with a speed of 18 m/s over water when it accidentally drops a 2 kg fish. Assuming the altitude of the bird is 5.4 m, and disregarding friction, what is the speed of the fish when it hits the water?

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