1. Describe the error in finding the component form of the vector u that has initial point (ˆ’3, 4) and terminal point (6, ˆ’1). The components are u1 = ˆ’3 ˆ’ 6 = ˆ’9 and u2 = 4 ˆ’ (ˆ’1) = 5. So, u = (ˆ’9, 5).

2. Describe the error in finding the direction angle of the vector v = ˆ’5i + 8j.
Because tan θ = b/a = 8/ˆ’5, the reference angle is θ' =|arctan (ˆ’8/5)| ‰ˆ |ˆ’57.99°| = 57.99° and θ ‰ˆ 360° ˆ’ 57.99° = 302.01°.

3. Prove that
(cos θ)i + (sin θ)j