Mathematics AA HL - Vectors

Every basic concept you need to know to level up and attempt the advanced questions for Vectors!

What does it mean if the scalar/dot product is greater than 0?

It means that the angle between the two vectors is acute.

What does it mean if the scalar/dot product is less than 0?

It means that the angle between the two vectors are obtuse.

What does it mean if the scalar/dot product is equal to 0?

Means that the angle between the vectors are perpendicular.

How do we find the angle between two vectors?

Using the formula, but first finding the scalar product to input into it.

What does it mean when lines are skew?

Skew is when lines do not intersect.

How to find the point of inflection on a graph

How do you find the point of inflection on a graph?

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The point of inflection on a graph is where the concavity changes. To find it, we need to find the second derivative of the function and set it equal to zero. Then, solve for x to get the x-coordinate of the point of inflection.

How do we find the normal given that we have the tangent?

-1/gradient

What does it mean if the tangent parallel to the x-axis mean?

It means that the gradient is equal to 0.

What happens if you dot product two times?

You get the magnitude squared.