What are Vectors?

Vectors are mathematical objects that have both magnitude and direction. Imagine arrows pointing in a particular direction with a certain length—those are vectors! They are commonly written as ordered lists of numbers, like \( \vec{v} = (3, 4) \).

Operations on Vectors

You can add two vectors by adding their corresponding components. You can also multiply a vector by a number (called a scalar) to stretch or shrink it.

• Vector Addition: \( (a_1, a_2) + (b_1, b_2) = (a_1 + b_1, a_2 + b_2) \)
• Scalar Multiplication: \( k(a_1, a_2) = (k a_1, k a_2) \)

Why Are Vectors Useful?

Vectors are everywhere! They're used to describe forces in physics, directions in navigation, and much more.

Practice Problems

• Add the vectors \( (1, 2) \) and \( (3, 4) \).
• Multiply the vector \( (2, -1) \) by \( 3 \).