This applet illustrates a vector in 3 dimensions defined by a magnitude and two angles. You can step through to see how the angles can be converted to coordinates along the three axes.[br][br]Step 1 - only the vector and controls are shown[br]Step 2 - Add the angles[br]Step 3 - Show a Rectangle from the origin to the vector tip perpendicular to the xz plane.[br]Step 4 - Show the component vector along the y axis[br]Step 5 - Show the component in the xz plane[br]Step 6 - Show a rectangle in the xz plane to the tip of the Fh vector[br]Step 7 - Show the component along the x axis[br]Step 8 - Show the component parallel to the z axis[br]Step 9 - Show the vector sum of the three components.

This applet illustrates a vector in three dimensions defined by its components. You can step through to see its properties.[br]Step 1 - Only the Vector and controls are shown[br]Step 2 - Show the x component[br]Step 3 - Add the y component[br]Step 4 - Add the z component[br]Step 5 - Show the vector as a sum of components[br]Step 6 - Show how the vector would be defined in a computer program[br]Step 7 - Define the magnitude of the vector[br]Step 8 - Define the unit direction vector[br]Step 9 - Show the unit vector inside a unit sphere[br]Step 10 - Show the components of the unit vector[br]Step 11 - Show the Direction Cosine for the x axis[br]Step 12 - Show the Direction Cosine for the y axis[br]Step 13 - Show the remaining direction cosine.[br][br]Note by the definitions:[br][math]\lambda_x^2+\lambda_y^2+\lambda_z^2=\cos^2\theta_x+\cos^2\theta_y+\cos^2\theta_z=1[/math]