Consider the force vector . If the magnitude of the torque is equal to the area of the equilateral triangle formed by the origin, , and , then determine the acute angle formed by and . Give your answer in degrees.
Let and be three non-zero vectors such that no two of them are collinear and . If is the angle between vectors and , then the value of is :
Let and be unit vectors and be a vector such that .
The angle in degrees between and such that is maximized is and the maximum value of is . Find the value of .
Suppose are three mutually perpendicular unit vectors.
Vector satisfies the equation
What is in terms of ?
Consider the regular octagon centered at the origin as shown at right. Eight unit vectors are drawn from the center of the octagon to each of its vertices and labeled in the figure. For each pair of distinct unit vectors with , their cross product is computed.
What is the sum of all of these cross products?