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## Vectors and Analytic Geometry in Space

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**Vectors and Analytic Geometry in Space**Dr. Ching I Chen**z=constant**(0,y,z) (0,0,z) P(x,y,z) (x,0,z) (0,y,0) O (x,0,0) y=constant (x,y,0) x=constant 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(1)Cartesian Coordinates To locate points in space, it uses three mutually perpendicular coordinate axes. The x-, y-, and z-axes shown there make a right-handed coordinate frame.**z**(0, 0, 5) (2,3,5) line y=3, z = 5 plane z=5 line x=2, z = 5 plane x=2 plane y=3 (0, 3, 0) (2, 0, 0) y x line x=2, y = 3 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(2)Cartesian Coordinates**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(3)Cartesian Coordinates To locate points in space, it uses three mutually perpendicular coordinate axes. The x-, y-, and z-axes shown there make a right-handed coordinate frame.**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(4, Example 1)Cartesian Coordinates**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(5, Example 2)Cartesian Coordinates**(0, 0, 1)**P(x, y, z) (0, 1, 0) (1, 0, 0) O 11.1Cartesian (Rectangular) Coordinates and Vectors in Space(6)Vector in Spaces**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(7)Vector in Spaces**O**11.1Cartesian (Rectangular) Coordinates and Vectors in Space(8, Example 3)Vector in Space**O**11.1Cartesian (Rectangular) Coordinates and Vectors in Space(9)Magnitude**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(10)Zero and Unit Vectors**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(11)Magnitude and Direction**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(12, Example 4)Magnitude and Direction**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(13, Example 5)Magnitude and Direction**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(14, Example 6)Magnitude and Direction**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(15)Distance and Spheres in Space**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(16, Example 7)Distance and Spheres in Space**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(17)Distance and Spheres in Space**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(18, Example 8)Distance and Spheres in Space**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(19, Example 9)Distance and Spheres in Space**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(20)Midpoints of Line Segments**11.1Cartesian (Rectangular) Coordinates and Vectors in**Space(21, Example 10) Midpoints of Line Segments**3**2 11.2 Dot Product (2, Example 1)Component Form**11.2 Dot Product (6, Theorem 1)Perpendicular (Orthogonal)**Vectors and Projections**11.2 Dot Product (7, Example 3)Perpendicular (Orthogonal)**Vectors and Projections**Q**B A S P R Q B A S R P 11.2 Dot Product (8)Perpendicular (Orthogonal) Vectors and Projections**11.2 Dot Product (9, Example 4)Perpendicular (Orthogonal)**Vectors and Projections**11.2 Dot Product (10, Exploration 1-1)Perpendicular**(Orthogonal) Vectors and Projections**11.2 Dot Product (11, Exploration 1-2)Perpendicular**(Orthogonal) Vectors and Projections**11.2 Dot Product (12, Exploration 1-3)Perpendicular**(Orthogonal) Vectors and Projections**11.2 Dot Product (13, Exploration 1-4)Perpendicular**(Orthogonal) Vectors and Projections**11.2 Dot Product (14, Exploration 1-5)Perpendicular**(Orthogonal) Vectors and Projections**B**A 11.2 Dot Product (15)Writing a Vector as a Sum of Orthogonal Vectors**11.2 Dot Product (16, Example 5)Writing a Vector as a Sum**of Orthogonal Vectors**F**D P Q 11.2 Dot Product (17)Work**F**D P Q 11.2 Dot Product (18, Example 6)Work**j**i k 11.3 Cross Products (4)Are Cross Products Commutative**B**h= |B||sin q| q A 11.3 Cross Products (5)|AB| Is the area of a parallelogram**3-ft bar**P Q 20-lb magnitude force F 11.3 Cross Products (7, Example 1)Torque**11.3 Cross Products (10, Example 2)Determinant Formula for**A × B