In Class Questions
MATH 151-Fall 02
September 3
1. Find the vector that represents moving from point A(2, -5) to point B(4, 3). What angle
does this vector make with respect to the positive x-axis?
vector =< 2, 8 >
angle = arctan( 82 ) ≈ 75.9637o
2. Find the vector that represents moving from point A(2, -5) to point B(-1, 5). What angle
does this vector make with respect the the positive x-axis?
vector =< −3, 10 >
o
angle = 90o + (90 − arctan( 10
3 )) ≈ 106.6992
3. A plane flies at a speed of 250km per hour in a direction of N30o W. (This means a direction
of 30o West of North.) Give the vector that represents this information.
→
−
a =< −250 cos 60o , 250 sin 60o > ≈ < −125, 216.506 >
4. A quarterback releases the football with a velocity of 50ft/sec at an angle of 35o with the
horizontal. Find the horizontal and vertical components.
horizontal component: 50 cos(35) = 40.9576
vertical component: 50 sin(35) = 28.6788
5. Which set of vectors are parallel?
(a) < 1, 6 > and < 6, 1 > not parallel
(b) < 2, 8 > and < 7, 28 > parallel
(c) < 6, −24 > and < −7.5, 30 > parallel
→
6. Is the vector −
a = 4i + 2j a unit vector? explain why or why not.
√
√
→
Since |−
a | = 42 + 22 = 20, this vector is not a unit vector.
→
−
7. Find a vector that has the opposite direction of b = 8i − 5j and a magnitude of 4.
√
→
−
| b | = 89.
−4 −
−32 20
→
The new vector will be √ b = √ , √
89
89 89