Vectors

Front

What is a vector?

Back

A vector is a quantity that has both magnitude and direction, represented graphically by an arrow.

Front

How do you find the angle between two vectors u and v?

Back

Use the formula: cos(θ) = (u • v) / (|u| |v|), where θ is the angle between the vectors, u • v is the dot product, and |u| and |v| are the magnitudes of the vectors.

Front

What is a unit vector?

Back

A unit vector is a vector with a magnitude of 1, indicating direction only.

Front

How do you find the unit vector in the direction of vector v?

Back

Divide the vector v by its magnitude: u = v / |v|.

Front

What is the formula for the magnitude of a vector v = ?

Back

The magnitude is given by |v| = √(x² + y²).

Front

How do you find the direction of a vector v = ?

Back

The direction θ can be found using θ = tan⁻¹(y/x).

Front

What is the component form of a vector from point R(x1, y1) to point S(x2, y2)?

Back

The component form is given by RS = .

Front

What is the dot product of two vectors u = and v = ?

Back

The dot product is u • v = u1*v1 + u2*v2.

Front

What is the cross product of two vectors in 3D?

Back

The cross product of vectors u = and v = is given by u × v = .

Front

What does it mean for two vectors to be orthogonal?

Back

Two vectors are orthogonal if their dot product is zero (u • v = 0).