Antiparallel

Definition

Antiparallel vectors are vectors that have the same magnitude but point in opposite directions. They are important in understanding vector subtraction and relative motion.

5 Must Know Facts For Your Next Test

1. Antiparallel vectors have a dot product that is negative.
2. The angle between antiparallel vectors is $180^\circ$ or $\pi$ radians.
3. In vector addition, adding antiparallel vectors results in a vector whose magnitude is the difference of their magnitudes.
4. If two forces are antiparallel, they produce a net force that is equal to the difference in their magnitudes.
5. Antiparallel displacement vectors can describe objects moving in opposite directions along the same path.

Review Questions

• What is the angle between two antiparallel vectors?
• How does the dot product of two antiparallel vectors compare to zero?
• What happens to the magnitude of the resultant vector when you add two antiparallel vectors?

Related terms

Vector Addition: The process of combining two or more vectors to produce their sum.

Dot Product: A scalar value obtained by multiplying corresponding components of two vectors and summing those products.

Magnitude: \\text{The length or size of a vector, often denoted as } \\|\\vec{A}\\|.