Definition --> a quantity with both ***magnitude*** and ***direction*** - force, acceleration, momentum, etc. ## Notation Indicated by an arrow: $\vec{F}$ - Concurrent - go through the same point - Coplanar - exist in the same plane - Resultant - combination of vectors ### Unit Vectors - Vectors with magnitude 1 that indicate direction - $x$ direction: $\hat{i}$ - $y$ direction: $\hat{j}$ - $z$ direction: $\hat{k}$ $ \vec{a}=6\hat{i}+2\hat{j}+7\hat{k} $ ### Matrix Form May also be represented as a vector: $ \vec{a}=6\hat{i}+2\hat{j}+7\hat{k}=\begin{bmatrix}6\\2\\7 \end{bmatrix} $ ## Magnitude $ |\vec{a}|=\sqrt{6^2+2^2+7^2}=\sqrt{89}\approx9.43 $ Generally: $ |\vec{F}|=\sqrt{\sum_iF_i^2} $ ## Operations - [[Vector Addition and Subtraction]] - [[Scalar (Dot) Product]] - [[Vector (Cross) Product]]