(b) c = ; d =
(c) e = ; f=
(d) g = ; h =
6.3 Solve for the unknown variables: (8, 3) + (b, 2) = (4, a).
(a) a =
(b) b =
6.4 Physicists model a magnetic field by assigning to every point in space a vector that represents the strength and direction of
the field at that point. Two magnetic fields that exist in the same region of space may be added as vectors at each point to find
the representation of their combined magnetic field. The "tesla" is the unit of magnetic field strength. At a certain point,
magnet 1 contributes a field of ( í6.4, 6.1, í3.7) tesla and magnet 2 contributes a field of (í1.1, í4.5, 8.6) tesla. What is the
combined magnetic field at this point?
( , , ) teslaSection 8 - Multiplying rectangular vectors by a scalar
8.1 Perform the following calculations.
(a) 6(3, í1, 8)
(b) í3(í3, 4, í5)
(c) ía(a,b,c)
(d) í2(a, 5, c) + 6 (3, íb, 2)
(a) ( , , )
(b) ( , , )
(c)
(d)
8.2 Three vectors that are neither parallel nor antiparallel can be arranged to form a triangle if they sum to (0, 0). (a) What vector
forms a triangle with (0, 3) and (3, 0)? (b) If you multiply all three vectors by the scalar 2, do they still form a triangle? (c) What
if you multiply them by the scalar a?
(a) ( , )
(b) Yes No
(c) Yes NoSection 9 - Multiplying polar vectors by a scalar
9.1 Perform the following computations. Express each vector in polar notation with a positive magnitude and an angle between 0°
and 360°.
(a) 2(4, 230°)
(b) í3(7, 20°)
(c) í4(8, 260°)
(a) ( , °)
(b) ( , °)
(c) ( , °)
9.2 A chimney sweep is climbing a long ladder that leans against the side of a house. If the displacement of her feet from the
base of the ladder is given by ( 2.1 ft, 65°) when she is on the third rung, what is the displacement of her feet from the base
when she has climbed twice as far?
( ft, °)(^64) Copyright 2007 Kinetic Books Co. Chapter 3 Problems