Statics ENGR 2214 Vectors in three dimensional space

Vectors in three dimensional space This figure shows the Right handed system, which is

Vectors in three dimensional space If the angle between F and its components (Fx)

Vectors in three dimensional space Also, if the angle between F and its components

Vectors in three dimensional space Similarly, if the angle between F and its components

Direction cosines cos , cos and cos are called: Direction cosines. y Fy F

Coordinates of points in space: The triplet (x, y, z) describes the coordinates of

Unit vector A unit vector along the line AB: A unit vector along the

A vector along A-B A vector F along the line A-B (and of magnitude

Dot Product: The dot product of vectors F and E is given by F

Parallelogram Law Two forces on a body can be replaced by a single force

Principal of Transmissibility The conditions of equilibrium or motion of a body remain unchanged

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

Vectors in three dimensional space 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). y 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 Fx, Fy, and Fz, respectively. Fy F j k Fz z Statics (ENGR 2214) Prof. S. Nasseri Fx i x

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

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

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

Direction cosines cos , cos and cos are called: Direction cosines. y Fy F j k Fz z Statics (ENGR 2214) Prof. S. Nasseri Fx i x

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 Statics (ENGR 2214) Prof. S. Nasseri

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

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

Parallelogram Law 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. Copyright of Ohio University 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 Statics (ENGR 2214) Prof. S. Nasseri