Vector Component

Intro to Vectors

By Elliot Moutra

​Vectors

​Many physical quantities, such as speed , can be completely described by a single real number called a scalar. This number indicates the magnitude or size of the quantity. A vector is a quantity that has both magnitude and direction.

• Ex: The velocity of a football is a vector that describes both the speed and direction of the ball.

• Ex: A boat traveling at 15 mph - scalar: has magnitude but no direction

• Ex: A hiker walking 25 paces due west - vector: has magnitude & direction

• Ex: a person's weight on a bathroom scale - vector: has magnitude & directions, gravity has a downward pull.

Multiple Choice

State whether each quantity described is a vector or scalar.

A car traveling 60mph 15⁰ east of south

• scalar

• vector

Multiple Choice

State whether each quantity described is a vector or scalar.

A parachutist falling straight down at 12.5mph

• scalar

• vector

Multiple Choice

State whether each quantity described is a vector or scalar.

A child pulling a sled with a force of 40 newtons

• scalar

• vector

​Vectors: Geometrically

• If a vector has its initial point at the origin, it is in standard position. The direction of a vector is the directed angle between the vector and the horizontal line that could be used to represent the x-axis.

​A & B can be represented as (x, y) points in the coordinate. We can take the values of A - (x₁, y₁) &

B - (x_2, y₂) and find the component form and magnitude of vector AB.

Vectors: Component Form <x₂ - x_1, y₂ - y₁>

​Qz: <7, -7>

​FORMULA

Vectors: Magnitude | v | = √ (x₂ - x₁)² + (y₂ - y₁)²

​Qz: <7, -7>, 9.9

Fill in the Blanks

Write the vector in component form.

$\overrightarrow{RS,}\ where\ R\ \left(-3,\ 9\right)\ \ S\ \left(8,\ -1\right)$  

Fill in the Blanks

Write the vector in component form and find its magnitude.

$\overrightarrow{PQ},\ P\ \left(-10,\ 5\right)\ Q\ \left(-9,\ -10\right)$  

Fill in the Blanks

Write the vector in component form and find its magnitude.

$\overrightarrow{AB},\ A\left(-2,\ 7\right)\ \ B\left(9,\ 5\right)$