When we write parametric equations of the plane we can easily find the direction vector. But for example if the equation is written like this x4y2z-10 we can find the normal vector by coefficThe algebraically imaginary part being geometrically constructed by a straight line or radius vector which has in general for each determined quaternion a determined length and determined direction in space may be called the vector part or simply the vector of the quaternion.The vector projection of a vector a on (or onto) a nonzero vector b (also known as the vector component or vector resolution of a in the direction of b) is the orthogonal projection of a onto a straight line parallel to b.It is a vector parallel to b defined as where is a scalar called the scalar projection of a onto b and b is the unit vector in the direction of b.
P (2 0 -2) on the given plane and you need two direction vectors. The direction vector for the line is d 2 i - k and a point on the line is Q (1 2 1) Its always a good idea to draw a sketch of the situation. From the sketch you can see immediately that one of the direction vectors for the plane can be d.This might seem strange but I cant really understand how to get direction vector for a given edge. For example 6(x10)7(y20)7z and the direction vector should be (766).Whether by accident or by design the plane of polarization has always been defined as the plane containing a field vector and a direction of propagation. In Fig. 1 there are three such planes to which we may assign numbers for ease of reference
From the above diagram the scalar magnitude of the projection on the plane is A sin() and its direction is along the plane (which is perpendicular to the normal B). To find the direction that we want first take a vector which is mutually perpendicular to A and B this is given by the cross product A x B (which is out of the page on the above diagram).A plane wave can be studied by ignoring the directions perpendicular to the direction vector that is by considering the function () () as a wave in a one-dimensional medium. Any local operator linear or not applied to a plane wave yields a plane wave.