Math 151 Week in Review Review of week 1 sections 1.1, 1.2
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1. For a   2 , 3
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and
J. Lewis
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b  1, 6 , find a  2 b .
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2. A parallelogram has adjacent sides given by the vectors v = 2 , 6 and w =  1, 5 .
Find vectors representing the diagonals of the parallelogram.
3. #28 pg 54 of the textbook.
Suppose that a wind is blowing from the direction N45Wat a speed of 50km/h. A pilot is
steering a plane in the direction N60E at the airspeed (speed in still air) of 250km/h. The
true course or track of the plane is the direction of the resultant of the velocity vectors of
the plane and the wind. The ground speed of the plane is the magnitude of the resultant.
Find the true course and the ground speed of the plane.
4. Similar to 29 pg 54 of the textbook. A man walks due east on the deck of a ship at 3.5
mph. The ship is moving in the direction N45E at 20 mph. Find the speed and direction
of the man relative to the water.
5. Similar to #30 in Stewart. Ropes of 3m and 5m lengths are fastened to a 5kg mass and
attached at different heights. The 3m rope is lower and makes an angle of 60 degrees to
the horizontal. the 5m rope makes an angle of 45 degrees. If gravity is rounded to
10m/sec^2, find the tension in the ropes.
6. Find the work done if a force of 20N applied at 30 degrees to the positive x-axis moves
an object:
a) 5 units to the right.
b) 7 units up.
c) from the origin to the point B(3,7).
7. Find the angle between the vectors 4 ,  4 and 1, 2 . Is this angle acute or obtuse?
What is the angle between  4 , 4 and 1, 2 . In general , if the angle between
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v and w is  , what is the angle between
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 v and w
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8. a) For the vectors v  2 , 1 and w   5 , 2 , find comp
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v
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 w  .
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Sketch the vectors and
the component.
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b) For the vectors in a) find proj   w  . Sketch the vectors and the projection.
v
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9. Using vectors, find the distance from the point P(3, 5) to the line 4x - 5y = 16.
10. Determine if the vectors are parallel, perpendicular, or neither.
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a) 5 i  6 j and 2 . 5 i  3 j
b) 5 i  6 j and  12 i  10 j
c) 5 i  6 j and  10 i  12 j
11. A line has slope 4. determine if the vector is parallel to the line, perpendicular to the
line or neither.
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a) 2 i  8 j
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b)  i  4 j
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c) 4 i  j
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d) 3 i  6 j