Adding/Subtracting Vectors - analytical method to add 2 vectors, add their respectie x and y components

• to substract 2 - substract their respective x and y compoennts.

Magnitude of A + B is sqrt((Ax + Bx)^2 + (Ay + By)^2) Direction = tan theta = (Ay + By) / (Ax + Bx)

Unit Vectors

Vectors of unit length (length 1) that paint along the xyz coord plane.

Must add to overall vector, A = Axi + Ayj + Azk

i-hat

x

j-hat

y

k-hat

z

Two-Dimensional Motion

Turn 2 dimensions into 2-one dimensions.

• Use both x and y coords - the coords have velocity and acceleration.
• Both axis move in one dimension.

There is no acceleration in the x-direction. Vx is velocity of x-coord along x-axis. Ax is acceleration of x-coord along the x-axis.

Total displacement and total velocity are directional properties. Direction of displacement is given by angle theta. Find magnitude of displacement or velocity by using pythagorean theorum.

Scalars

Just numbers (mass, volume)

Vectors

Displacement, velocity, acceleration are all directional properties - vector properties.

Have both a abs value magnitude and direction.

Are represented by a directional arrow.

The pythagorean theorum can be used for 3 sides in 3 dimensions! sqrt(A^2 + B^2 + C^2)