Vectors

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In physics, quantities are classified using two categories: scalar quantities and vector quantities. Scalar quantities are defined purely by its magnitude. Examples of scalar objects include mass, speed, and distance. Vector quantities are defined by its magnitude and also by direction. Hence the definition of a vector; it is an arrow which gives direction and the size of the arrow gives its magnitude. Some examples include force, torque, velocity, acceleration and momentum.

In this website, we will utilize vector mathematics for calculations.  An important equation in the later section involves the cross product of two vectors. Geometrically speaking, a cross product of two vectors gives a third vector which is perpendicular to the both vectors. The right-hand rule is applied when determining the direction of the cross product vector.

Right Hand Rule:

• Place your right hand on the first vector, end of your palm must be positioned on the initial point of the vector
• Curl your hand towards the second vector
• The direction in which your thumb is pointing is the direction of the cross product of the two vectors

This animated diagram shows the cross product of vectors x and y.  It follows the right hand rule. To learn more about vector mathematics and geometry, go to Vector Analysis


Sample Problem
What is the cross product of v and w, if v = <4, 3, 5> and w = <6, 2, 3>?

Your Answer:

Solution