10.2 Space Coordinates and Vectors in Space

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Presentation transcript:

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

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)

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!!!

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

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?

Does this formula look familiar???

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?

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

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