Presentation is loading. Please wait.

Presentation is loading. Please wait.

10.2 Space Coordinates and Vectors in Space

Similar presentations


Presentation on theme: "10.2 Space Coordinates and Vectors in Space"— Presentation transcript:

1 10.2 Space Coordinates and Vectors in Space
3D Coordinate System Vectors in Space Real life applications

2 Review from 10.1 Two vectors are equal if they have the same magnitude and direction (same length and are parallel) The zero vector, denoted by 0, is a vector with zero magnitude (undefined direction)

3 More about vectors Two nonzero vectors u and v are parallel if there is some scalar c such that u=cv. Parallel vectors can be used to show collinearity. Vectors that go in opposite directions can also be considered parallel!!!

4

5

6

7 Show that the triangle with vertices given by P = (2, 1, 6), Q = (4, 7, 9), and R = (8, 5, -6) is a right triangle. (Use the fact that a right triangle must satisfy the Pythagorean Theorem

8 Consider the triangle whose corners are the points
Can extend the distance formula to determine if a triangle is isosceles or right triangles! Consider the triangle whose corners are the points P = (1, 1,-1), Q = (2, -1, 1), R = (4, 1, 2) Is the triangle isosceles or right?

9 Does this formula look familiar???

10

11 Find an equation of a sphere with radius 3 and center at (2, -1, 0)
Find an equation of a sphere with radius 3 and center at (2, -1, 0). Is the origin inside this sphere?

12

13

14 Find the equation of the sphere that has the line segment between
(-2, 3, 6) and (4, -1, 5) as its diameter.

15

16 Homework/Classwork Pg. 732 #5, 7, 27, 29, 35, 37, 39, 41, 51, 57, 59, 61, 63, 67, 69, *71, 75, AND 83


Download ppt "10.2 Space Coordinates and Vectors in Space"

Similar presentations


Ads by Google