7.++Cartesian+Vectors

Cartesian Vectors
May 7th Corinne Brassem Dot Product and Projections of a Vector:

Homework: pg. 55-58 # 1, 6, 8, 10, 12, 18, 19 pg. 64-65 # 2, 5, 10-12

Extra Links:
 * Dot Product: http://mathworld.wolfram.com/DotProduct.html
 * Projections of a Vector: http://www.vitutor.com/geometry/vec/vector_projection.html

//Corina Lee//
 * May 8th**



I COULDN'T GET THE DRAWING UP ON THE SAME FILE.. sorry guys! :( Here is the first drawing that goes under the "draw point A"



Each tick is one unit!

And the second drawing for vector OB:

pg 81-83 #2-4, 6-12
 * Homework:**

For notes: http://tutorial.math.lamar.edu/Classes/CalcIII/3DCoords.aspx
 * Extra links:**

For homework: Watch this until 0:45 to get a better understand of 3D: www.youtube.com/watch?v=IqIiZAaH-Oo

Then watch this! It will clear a lot of things up :) http://www.youtube.com/watch?v=ySS3OHE6_c8&feature=related

Math quiz on Tuesday, test on Friday!
 * Reminders:**

May 9th Alysha Sawyer Operations with Vectors in 3 Space Adding, subtracting, and multiplying by a constant for vectors in 3D are exactly the same as in 2D. Ex. and = (5, -4, -4) Ex. and = (1, 4, -6) Ex. k= -2 Coplanar and Linearly Dependent Given vectors and scalars a and b. If then the vectors are linearly dependent and coplanar. If coplanar always linearly dependent and vise versa. Ex. Determine if the following vectors are coplanar. , If a and b exist than the vectors are coplanar. To determine if they exist make 3 equations using the x, y and z co-ordinates. -1= 3a -9b -2 = -a -4b 1 = a+b Add 1 = a +b

1 = 3b b = 1/3 Sub b = 1/3 into equation an equation 1 = a+b 1 = a + 1/3 a = 2/3 Check your answer with the equation not yet used -1 = 3a – 9b LS = -1 RS= 3a -9b =3(2/3) – 9(1/3) =-1 Therefore LS=RS so the three vectors are coplanar Homework on page 88-90 #1, 3, 9, 15ab, 17ab Links [] The first part of this link is good if you are having troubles with adding vectors and mutliplying by a scalar. [] This link goes through a lot more examples for coplanar.

May 11th - Eisha Dot Product in 3D space

Geoff, May 14



[] []

Rochelle, May 15

May 16th Anthony (switched with Charlie for May 30th) Test Number 7 Cartesian Vectors Answer Key