Warm-Up Draw a diagram that shows the resolution of each vector into its rectangular components. Then find the magnitudes of the vector’s horizontal and vertical components. 1.5 centimeters at a bearing of 𝑁 49 𝑜 𝐸 ¾ inch per minute at a bearing of 255 𝑜 Aiko is pushing the handle of a push broom with a force of 190 N at an angle of 33 𝑜 with the ground. Draw a diagram that shows the resolution of this force in its rectangular components. Find the magnitude of the horizontal and vertical components.

Vectors in the Coordinate Plane

Standard Position Last class, we wrapped up with finding the horizontal and vertical components of vectors A vector 𝑂𝑃 in standard position on a coordinate plane can be described by the coordinates of its terminal point P(x,y). x and y are rectangular components 𝑥,𝑦 is the component form of the vector

Some Vectors are more Equal than others Vectors with the same magnitude and direction are equivalent, and can be represented by the same coordinates The component form of a vector 𝐴𝐵 with initial point 𝐴( 𝑥 1 , 𝑦 1 ) and terminal point 𝐵( 𝑥 2 , 𝑦 2 ) is given by 𝑥 2 − 𝑥 1 , 𝑦 2 − 𝑦 1

Can you find it? Find the component form of 𝐴𝐵 with the given initial and terminal points. A(-4,2), B(3,-5) A(-2,-7), B(6,1) A(0,8), B(-9,-3)

Keeping a safe distance If v is a vector with initial point ( 𝑥 1 , 𝑦 1 ) and terminal point ( 𝑥 2 , 𝑦 2 ), then the magnitude of v is given by 𝒗 = 𝑥 2 − 𝑥 1 2 + 𝑦 2 − 𝑦 1 2 Alternatively, since you have a right triangle, you can use:

Find the magnitude of 𝐴𝐵 with the given initial and terminal points. A(-4,2), B(3,-5) A(-2,-7), B(6,1) A(0,8), B(-9,-3)

Operations for the minions If 𝒂= 𝑎 1 , 𝑎 2 and 𝒃= 𝑏 1 , 𝑏 2 are vectors and k is scalar, then: Vector Addition: 𝒂+𝒃= 𝑎 1 + 𝑏 1 , 𝑎 2 + 𝑏 2 Vector Subtraction: 𝒂−𝒃= 𝑎 1 − 𝑏 1 , 𝑎 2 − 𝑏 2 Scalar Multiplication 𝑘𝒂= 𝑘 𝑎 1 ,𝑘 𝑎 2

I’m going bananas Find each of the following for 𝒘= −4,1 , 𝒚= 2,5 and 𝒛= −3,0 w + y z – 2y 4w + z - 3w 2w + 4y - z

Some Conversions When given the magnitude and direction of a vector, you can rewrite it in component form. Find the component form of v with the given magnitude and direction angle. 𝒗 =10, 𝜃= 120 𝑜 𝒗 =8, 𝜃= 45 𝑜 𝒗 =24, 𝜃= 210 𝑜

Dave, running forward at 5 meters per second, throws a football with a velocity of 25 meters per second at an angle of 40 𝑜 with the horizontal. What is the resultant speed and direction of the pass? What would the resultant velocity of the football be if the quarterback made the same pass running 5 meters per second backward?