# In Class Questions MATH 151-Fall 02 September 5 ```In Class Questions
MATH 151-Fall 02
September 5
Some definitions also found in Stewart:
−
→
The orthogonal compliment of the vector →
a =&lt; a1 , a2 &gt; is −
a ⊥ =&lt; −a2 , a1 &gt;
The scalar projection of vector b onto a, denoted compa b =
projection of b onto a.
→
−
−
→
a &middot; 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. &lt; 4, 5 &gt; and &lt; −10, 5 &gt;
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) =&lt; 1, 1 &gt; +t &lt; 5, 9 &gt;
→
−
r2 (s) =&lt; 3, −2 &gt; +s &lt; 6, 7 &gt;
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