Magnitude

Definition

Magnitude is the size or length of a vector, representing its absolute value. It is always a non-negative scalar quantity.

5 Must Know Facts For Your Next Test

1. Magnitude is calculated using the Pythagorean theorem when dealing with vectors in two or three dimensions.
2. For a vector $\mathbf{A} = (A_x, A_y, A_z)$, its magnitude is given by $|\mathbf{A}| = \sqrt{A_x^2 + A_y^2 + A_z^2}$.
3. Magnitude does not convey any information about the direction of the vector.
4. In physics problems, magnitude can represent quantities such as displacement, velocity, or force without specifying direction.
5. When vectors are multiplied by scalars, only the magnitude changes while the direction remains unchanged.

Review Questions

• How do you calculate the magnitude of a vector given its components?
• Why is it important to differentiate between magnitude and direction in physics problems?
• What happens to the magnitude of a vector if it is multiplied by a scalar?

Related terms

Vector:

A quantity that has both magnitude and direction.

Scalar:

A quantity that has only magnitude and no direction.

Unit Vector:

A vector with a magnitude of one used to indicate direction.