Suppose vectors A and B are rotated in the plane which contains them. What happens to the direction of vector C = A × B
Answers
Answer:
To find a unit vector with the same direction as a given vector, we divide by the magnitude of thevector. For example, consider the vector v = (1, 3) which has a magnitude of . If we divide each component of v by we will get the unit vector uvwhich is in the same direction as v: .
Answer:
Well, rotated though certain degree. It sounds like you rotate the vector in a euclidean plane. This is the more trivial example of a change of coordinates. If you do a rotation of a vector in a euclidean plane the new coordinates when a turn of angle \phi in antihorary sense the transformation of coordinates can be written (writing the components of the vector in a column matrix) is given by the formula
If you wish to know the transformation of the vector for a more general movement of it, or a vector in more dimension. Of course, there are formulas for movements of vector in space, and in any reimann space where the metric tensor is not constant, you can replantate the question, but for a turn in a plain, in the same system of reference , the change of the vector is trought this fomula