Vektoren

Question 1

How do you find a vector, given two points?

Answer 1

You subtract the start point from the endpoint.

Question 2

How do you draw vector addition?

Answer 2

1. Draw the first vector from the starting point (usually the origin).
2. Starting at the end arrow of step 1, draw the second vector.
3. The addition vector is the vector that connects the very start point with the endpoint of the second vector.

Question 3

How do you draw vector subtraction?

Answer 3

1. Draw the first vector from the starting point (usually the origin).
2. Starting at the end arrow of step 1, draw the second vector BACKWARDS. (the negative version)
3. The subtraction is the vector that connects the very start point with the endpoint of the second vector.

Question 4

How do you multiply scalars with vectors?

Answer 4

The scalar multiplies each component of the vector.

Question 5

What are the two different ways to multiply vectors?

Answer 5

1. Dot product (also known as Scalar product)
2. Cross product

Question 6

What is the difference between a dot product (scalar product) and a cross product?

Answer 6

1. The outcome of a dot product is just one single number.
2. The outcome of a cross product is a new (normal) vector.

Question 7

How do you find the dot product of two vectors?

Answer 7

Add together the product of the matching components from each vector.

Question 8

How do you find the cross product of two vectors?

Answer 8

Question 9

How do you find a normal vector to two vectors (at the same time)?

Answer 9

You take the cross product of those two vectors.

Question 10

How do you find the normal vector to this line?

Answer 10

Each component of the normal vector is simply that component’s coefficient from the equation.

Question 11

How do you find the normal vector to this Ebene?

Answer 11

Each component of the normal vector is simply that component’s coefficient from the equation.