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Scalars and Vectors
Scalar: A quantity like mass or temperature which only has a magnitude Vector: A quantity like heat flux or force which has both a magnitude and a direction (denoted by a bold faced character, an underlined character, or a character with a arrow on it) Vector Addition: Vector Addition follows the parallelogram law described be the figure
Resolution of a Vector: A vector can be resolved along different directions using the parallelogram rule. The figure shows how one resolves vector c into components a and b which are along the given directions
The math you need: o For a right triangle:
a 2 + b^2 = c^2
tan() = b/a
sin() = b/c
cos() = a/c
o For a general triangle:
Sine law:
Cosine law:
o A line intersecting parallel lines:
Vectors in 3-D
Unit vector: A vector of unit length.
Base vectors for a rectangular coordinate system: A set of three mutually orthogonal unit vectors
Right handed system: A coordinate system represented by base vectors which follow the right-hand rule.
Rectangular component of a Vector: The projections of vector A along the x, y, and z directions are Ax, Ay, and Az , respectively.
Magnitude of a Vector:
Direction Cosines: Cos( Cos( Cos(
A unit vector along the line A-B : A unit vector along the line A-B is obtained from
A vector along A-B : A vector F along the line A-B and of magnitude F can be obtained from
The dot product: The dot product of vectors A and B is given by
Projection of a vector by using the dot product: The projection of vector A along the unit vector u is given by
Examples:
