Practice Projection in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The image formed when points of a shape are mapped onto a lower-dimensional surface along parallel or converging rays.
A shadow cast on the ground is a projection—a 3D object mapped down to a 2D silhouette.
Example 1
mediumFind the orthogonal projection of point P(3, 7) onto the x-axis, the y-axis, and the line y = x.
Example 2
hardVector \vec{a} = (3, 4) is projected onto vector \vec{b} = (1, 0). Find (a) the scalar projection and (b) the vector projection. Then find the projection onto \vec{c} = (1, 1)/\sqrt{2}.
Example 3
easyA 5 m flagpole stands vertically. At 3 pm the sun casts a horizontal shadow 12 m long. What is the length of the shadow (the projection of the pole onto the ground)?
Example 4
hardProject the vector \vec{v} = (2, -1, 3) onto the unit vector \hat{u} = (0, 0, 1) (the z-axis direction). Interpret the result geometrically.