VECTORS in 3-D Space Vector Decomposition Addition of Vectors: Fx, Fy, Fz Addition of Vectors: Cartesian Vector Form: Unit Vectors:

Vectors in 3-D Space: Vector Components Fx = |F| cos x Fy = |F| cos y Fz = |F| cos z z F Fz y Fy Fx x

Cartesian Representation Cartesian Vector Form: Vector Components Fx = |F| cos x Fy = |F| cos y Fz = |F| cos z Magnitude Directional Cosines: Trigonometry Identity cos x = cos y = cos z= cos2x + cos2y + cos2 z = 1

Cartesian Representation Cartesian Form:

Different Problems Case 1:

Activity #1: Write the vectors F1, F2 in cartesian vector: (just write equation without doing calculations). Using Maple add vectors F1, F2 to find R. Using Maple Find Magnitude of R

Unit Vector in Direction of F: Cartesian Vector Form Unit Vector, eF , in Direction of F: Dividing Above Eqn by its magnitude: But, since we know:

Unit Vector So, a unit vector is given by a vector F: Or by its directional cosines: To find

Activity #2: For previous activity find using MAPLE (a) Unit vector in direction of F: eF (b) Magnitude of the Unit Vector: eF (c) Angle of Resultant force R:

Unit Vector from Position In some case the angles of a vector are not given, neither the components of force. ONLY know: z A(3,-4,5 F=10N y x

Activity #3 Solve Problem 2.81 using MAPLE. Follow the example given in Class Class of Prob. 2.80