Scalar and Vector Projections

Consider the question from above.

The definition of vector projection for the indicated red vector is the called projuv. When you read projuv, you should say "the vector projection of v onto u." This implies that the new vector is going in the direction of u. The vector projection is the vector produced when one vector is resolved into two component vectors, one that is parallel to the 2nd vector and one that is perpendicular to the 2nd vector. The parallel vector is the vector projection. Conceptually, this means that if someone is pulling the box at an angle and strength of vector v, then some of their energy would be wasted pulling the box up, and some of their energy would actually contribute to pulling the box horizontally.

"SINNERS" in Purple Hibiscus

1 - the right angle triangle