Section 3.3: Vectors: Dot Product

Problem Types

Projection Practice

Compute the projection of $a = \langle 1,2,1 \rangle$ onto $u = \langle 0, 1, -1\rangle$.

Compute the projection of $u$ onto $a$.

Solution

Projection Problem

Find the point on the line $y = 3x$ closest to the point $(1,1)$.

Projection Problem

An object is traveling due east at a speed of 5 m/s. A wind is blowing in a northwestern direction with a constant force of 2N. How much work is done by the wind over a span of 30 s?

Solution