1. Statics (ENGR 2214) Prof. S. Nasseri Statics ENGR 2214 Vectors in three dimensional space

2. Statics (ENGR 2214) Prof. S. Nasseri This figure shows the Right handed system, which is a coordinate system represented by base vectors which follow the right-hand rule (four fingers from x to y, and thumb will be along z direction). Vectors in three dimensional space Base vectors for a rectangular coordinate system: A set of three mutually orthogonal unit vectors Rectangular component of a Vector: The projections of vector F along the x, y, and z directions are F x, F y, and F z, respectively. F FxFx FyFy i j x y k z FzFz

3. Statics (ENGR 2214) Prof. S. Nasseri Vectors in three dimensional space If the angle between F and its components (F x ) on axis x is , then F FxFx i x y z

4. Statics (ENGR 2214) Prof. S. Nasseri Vectors in three dimensional space Also, if the angle between F and its components (F y ) on axis y is , then F FyFy j x y z

5. Statics (ENGR 2214) Prof. S. Nasseri Vectors in three dimensional space Similarly, if the angle between F and its components (F z ) on axis z is , then F x y k z FzFz 

6. Statics (ENGR 2214) Prof. S. Nasseri Direction cosines cos , cos  and cos  are called: Direction cosines. F FxFx FyFy i j x y k z FzFz

7. Statics (ENGR 2214) Prof. S. Nasseri Coordinates of points in space Coordinates of points in space: The triplet (x,y,z) describes the coordinates of a point. The vector connecting two points: The vector connecting point A to point B is given by

8. Statics (ENGR 2214) Prof. S. Nasseri Unit vector A unit vector along the line A- B: A unit vector along the line A-B is obtained from

9. Statics (ENGR 2214) Prof. S. Nasseri A vector along A-B A vector F along the line A-B (and of magnitude F) can be obtained from

10. Statics (ENGR 2214) Prof. S. Nasseri Dot Product Dot Product: The dot product of vectors F and E is given by Projection of a vector by using the dot product: The projection of vector F along the unit vector u is given by  F E  F u F.u

11. Statics (ENGR 2214) Prof. S. Nasseri Parallelogram Law Copyright of Ohio University Two forces on a body can be replaced by a single force called the resultant by drawing the diagonal of the parallelogram with sides equivalent to the two forces.

12. Statics (ENGR 2214) Prof. S. Nasseri Principal of Transmissibility The conditions of equilibrium or motion of a body remain unchanged if a force on the body is replaced by a force of the same magnitude and direction along the line of action of the original force. Copyright of Ohio University