Operations with Vectors

Front

What is a vector?

Back

A vector is a quantity that has both magnitude and direction, represented as an ordered pair (x, y) in a coordinate system.

Front

How do you add two vectors?

Back

To add two vectors, you add their corresponding components. For example, if u = 〈u1, u2〉 and v = 〈v1, v2〉, then u + v = 〈u1 + v1, u2 + v2〉.

Front

What is a unit vector?

Back

A unit vector is a vector with a magnitude of 1, often used to indicate direction.

Front

How do you find a unit vector in the opposite direction of a given vector?

Back

To find a unit vector in the opposite direction of vector a = 〈a1, a2〉, first find its magnitude |a| = √(a1² + a2²), then the unit vector is -a/|a|.

Front

What is the formula for the magnitude of a vector?

Back

The magnitude of a vector a = 〈a1, a2〉 is given by |a| = √(a1² + a2²).

Front

How do you subtract two vectors?

Back

To subtract two vectors, you subtract their corresponding components. For example, u - v = 〈u1 - v1, u2 - v2〉.

Front

What does it mean for two vectors to be parallel?

Back

Two vectors are parallel if they have the same or opposite direction, which means one is a scalar multiple of the other.

Front

What is the dot product of two vectors?

Back

The dot product of vectors u = 〈u1, u2〉 and v = 〈v1, v2〉 is calculated as u • v = u1*v1 + u2*v2.

Front

What is the cross product of two vectors?

Back

The cross product of two vectors in three-dimensional space results in a vector that is perpendicular to both. It is defined as u × v = |u||v|sin(θ)n, where θ is the angle between u and v.

Front

How do you find the resultant vector of two vectors?

Back

The resultant vector is found by adding the two vectors together using vector addition.