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Unformatted text preview: e following quantities vectors or scalars? Explain. (a)
(d) ❙❙❙❙ 6, 2,
j k ■ ■ ■ ■ Find a unit vector that has the same direction as the given vector.
23. S R 9, 25. 8 i 5. Copy the vectors in the ﬁgure and use them to draw the following vectors.
(a) u v
(c) v w (b) u
(d) w u v ■ 24. 12 i 5
j ■ 5j 4k
■ ■ ■ ■ ■ ■ ■ 26. Find a vector that has the same direction as v
v ■ ■ 2, 4, 2 but has length 6. u 27. If v lies in the ﬁrst quadrant and makes an angle positive x-axis and v w 3 with the
4, ﬁnd v in component form. 28. If a child pulls a sled through the snow with a force of 50 N
6. Copy the vectors in the ﬁgure and use them to draw the follow- ing vectors.
(a) a b
(c) 2 a
(e) 2 a b (b) a b
(d) 1 b
(f) b 3 a a exerted at an angle of 38 above the horizontal, ﬁnd the
horizontal and vertical components of the force.
29. Two forces F1 and F2 with magnitudes 10 lb and 12 lb act on an object at a point P as shown in the ﬁgure. Find the
resultant force F acting at P as well as its magnitude and its
direction. (Indicate the direction by ﬁnding the angle shown
in the ﬁgure.)
F b F¡
7–12 Find a vector a with representation given by the directed
line segment AB. Draw AB and the equivalent representation starting at the origin. F™ |||| 7. A 2, 3 , B 2, 1 8. A 2, 2, B 5, 3 ¨
P ■ 5E-13(pp 838-847) 842 ❙❙❙❙ 1/18/06 11:14 AM Page 842 CHAPTER 13 VECTORS AND THE GEOMETRY OF SPACE 30. Velocities have both direction and magnitude and thus are 37. (a) Draw the vectors a vectors. The magnitude of a velocity vector is called speed.
Suppose that a wind is blowing from the direction N45 W at a
speed of 50 km h. (This means that the direction from which
the wind blows is 45 west of the northerly direction.) A pilot
is steering a plane in the direction N60 E at an airspeed (speed
in still air) of 250 km h. The true course, or track, of the plane
is the direction of the resultant of the velocity vectors of the
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This note was uploaded on 02/04/2010 for the course M 56435 taught by Professor Hamrick during the Fall '09 term at University of Texas at Austin.
- Fall '09