Vectors: Magnitude & Direction

Front

What is the definition of a vector?

Back

A vector is a quantity that has both magnitude and direction.

Front

How do you find the magnitude of a vector represented as ?

Back

The magnitude of a vector is calculated using the formula √(x² + y²).

Front

What is the component form of a vector?

Back

The component form of a vector is expressed as , where x and y are the horizontal and vertical components, respectively.

Front

Given points A(2, 4) and B(-8, 7), how do you find the vector AB?

Back

The vector AB is found by subtracting the coordinates of A from B: AB = = <-10, 3>.

Front

What is the magnitude of the vector <10, -8>?

Back

The magnitude is calculated as √(10² + (-8)²) = √(100 + 64) = √164 ≈ 12.81.

Front

What does it mean for a vector to have a negative component?

Back

A negative component indicates direction; for example, a negative y-component means the vector points downward.

Front

How do you represent a vector graphically?

Back

A vector is represented graphically as an arrow, where the length indicates magnitude and the direction of the arrow indicates direction.

Front

What is the difference between scalar and vector quantities?

Back

Scalar quantities have only magnitude (e.g., temperature), while vector quantities have both magnitude and direction (e.g., velocity).

Front

How do you add two vectors graphically?

Back

To add two vectors graphically, place the tail of the second vector at the head of the first vector and draw a new vector from the tail of the first to the head of the second.

Front

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

Back

The dot product of vectors A and B is calculated as A • B = |A| |B| cos(θ), where θ is the angle between them.