Exercise 3.4.2. Given two orthonormal vectors and and the vector , project onto and . Also find the projection of onto the plane formed by and .

Answer: Since is orthonormal, the projection of onto is given by

Similarly the projection of onto is given by

The projection of onto the plane formed by and is simply the sum of the projections above:

NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.

If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fifth Edition and the accompanying free online course, and Dr Strang’s other books.