In Class Questions
MATH 151-Fall 02
September 5
Some definitions also found in Stewart:
−
→
The orthogonal compliment of the vector →
a =< a1 , a2 > is −
a ⊥ =< −a2 , a1 >
The scalar projection of vector b onto a, denoted compa b =
projection of b onto a.
→
−
−
→
a · b
, is the length of the vector
→
|−
a|
→
−
1. Find a vector that is orthogonal to b = 4i − 5j.
2. Find the angle between these vectors. < 4, 5 > and < −10, 5 >
3. Find the vector equation and the parametric equation of the line thru the points (8, 7) and
(10, 5).
4. Find the distance between the point (−1, 1) and y = −4x + 12
5. Sketch the graph and give the Cartesian equation of the curve defined parametrically as
x(t) = 3 cos θ and y(t) = 2 sin θ and 0 ≤ θ ≤ π.
6. Are these lines parallel? perpendicular? Do they intersect and if yes then where?
→
−
r1 (t) =< 1, 1 > +t < 5, 9 >
→
−
r2 (s) =< 3, −2 > +s < 6, 7 >