You will need
- - the concept of the Cartesian coordinate system;
- - trigonometric functions;
- - action vectors.
Draw a vector or a line segment in the coordinate system. Then, from one end of the segment or vector drop perpendiculars to each of the axes. At the intersection of the perpendicular and each axis mark the point. Repeat this procedure for the second end of the segment or vector.
Measure the distance from the origin to each point of intersection with the coordinate system. On each axis from a greater distance, subtract the least - this will be the cut or projection of the vector on each of the axles.
If you know the coordinates of the ends of the vector or line segment to find its projection on the axis, from the coordinates of the end subtract the corresponding coordinates of the beginning. If the value is negative, take its module. The minus sign indicates that the projection is in the negative part of the coordinate axis. For example, if the coordinates of beginning of vector (-2;4;0) and the coordinates of the end (2;6;4), the projection on the axis OX is equal to 2-(-2)=4, on the OY axis: 6-4=2 on axis OZ: 4-0=4.
If the coordinates of the vector, then they are the projections on the respective axis. For example, if the vector has coordinates (4;-2;5), it means that the projection on the axis OX equal to 4, on the OY axis: 2 axis OZ: 5. If the coordinate vector is 0, and its projection on this axis is also equal to 0.
In that case, if you know the length of the vector and the angle between it and the axis (in polar coordinates), in order to find its projection on this axis, you need to multiply the length of this vector on tothe axis of theNUS of the angle between the axis and the vector. For example, if it is known that the vector length is 4 cm and the angle between him and the OX axis in the coordinate system XOY is equal to 60º.
To find its projection on the OX axis, multiply by 4 cos(60º). Calculation 4•cos(60º)=4•1/2=2 cm, Find the projection on the OY axis by finding the angle between it and the vector 90º-60º=30º. Then its projection on this axis will be 4•cos(30º)=4•0,866=3,46 cm