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 calculate the magnitude of a vector represented as ?

Back

Magnitude = √(x² + y²) where x and y are the components of the vector.

Front

What is the direction of a vector ?

Back

Direction = tan⁻¹(y/x) (adjusted based on the quadrant of the vector).

Front

What are the horizontal and vertical components of a vector with magnitude |v| and angle θ?

Back

Horizontal component = |v| * cos(θ), Vertical component = |v| * sin(θ).

Front

How do you find the angle of a vector in standard position?

Back

The angle θ can be found using θ = tan⁻¹(y/x) and adjusting for the correct quadrant.

Front

What is the formula for the dot product of two vectors and ?

Back

Dot product = a*c + b*d.

Front

What is the significance of the dot product being zero?

Back

If the dot product of two vectors is zero, the vectors are orthogonal (perpendicular to each other).

Front

How do you find the resultant vector of two vectors A and B?

Back

Resultant vector R = A + B, calculated by adding corresponding components.

Front

What is the unit vector in the direction of a vector ?

Back

Unit vector = , where |v| is the magnitude of the vector.

Front

What is the angle between two vectors A and B?

Back

The angle θ can be found using cos(θ) = (A·B) / (|A| * |B|).