**Question 1: **Explain how vectors and mathematics are used in GPS technology.

**Question 2: **Given two vectors a and b, find:

a) when is the magnitude of a+b more than that of a-b?

b) when is the magnitude of a+b less than that of a-b?

c) when is the magnitude of a+b equal to that of a-b?

d) when is la+bl=lal+lbl?

e) what is the minimum value of la+bl?

**Question 3:** Explain the meanings of the terms linearly dependent and coplanar. Make sure you demonstrate that you understand the difference between the terms, and the situation in which linear dependency implies coplanarity.

**Question 4:** Give examples of THREE vectors that are collinear and prove it.

**Question 5:** Given a=[1, -3, 6] and b=[4, -5, -2], find a vector c so that a*(bxc)=0. Explain what is the relationship between the vectors a, b, and c in this case, and why? VERIFY THIS.

**Question 6:** a, b, and c are vectors. Prove that a*(b+c)=a*b+a*c for all a, b, c ∈ R^{3}

**Question 7:** DRAW DIAGRAMS to explain the answers to the following questions.

a) Is it possible to have *p*_{a}(b)=0 ?

b) Is it possible to have *p*_{a}(b) undefined?

c) Is it possible to have *p*_{a}(b)= *p*_{b}(a) ?

e) Explain why* p*_{a}(c)=*p*_{a}(*p*_{b}(c))?

**Question 8: **The position of a point on a line is given by the equation s(t)=t^3-6t^2+9t-4, where s is measured in meters and t in seconds. After 2 seconds, is it moving toward or away from the origin? Show your work.

**Question 9: **Water is leaking from a trough at the rate of 0.8 L/s. The trough has a trapezoidal cross section, where the width at the bottom is 55cm, at the top 85cm, and the height is 25cm. The length of the trough is 3m. Find the rate at which the height is changing when the depth of water is 11cm. INCLUDE A DIAGRAM.

### Recently Asked Questions

- How is the amount of oxygen limited in its bonding to HB by the pH of the blood and the amount of carbon monoxide in blood

- Graph #5: Long-run Profit or Loss (use MC, AR, ATC, and AR; shade where appropriate) Please use my following essay passage to make a graph of a demand

- · How does the amount of oxygen bond to HB vary with the amount of oxygen in human blood, such as in the partial pressure exerted by oxygen?