AP Physics C Adding Vectors
(1) Find the (a) x, (b) y, and (c) z components of the sum r displacements c and d
whose components in meters along the three axes are cx =7.4, cy = -3.8, cz = -6.1;
dx = 4.4, dy = -2.0, dz = 3.3.
(2) Vector a has a magnitude of 5.0m and is directed east. Vector b has a magnitude
of 4.0m and is directed 35o west of north. What are (a) the magnitude and (b) the
direction of a + b? What are (c) the magnitude and (d) the direction of b - a? (e)
Draw a vector diagram for each situation.
(3) For the vectors a = (3.0m)i + (4.0m)j and b = (5.0m)i + (-2.0m)j give a + b in (a)
unit-vector notation, and as (b) a magnitude and (c) an angle. Now give b - a in
(d) unit-vector notation, and as (e) a magnitude and an (f) angle.
(4) Two vectors are given by
a = (4.0m)i – (3.0m)j + (1.0m)k and b = (-1.0m)i + (1.0m)j + (4.0m)k
In unit-vector notation, find (a) a + b, (b) a – b, and (c) a third vector such
that
a-b+c=0
(5) What is the sum of the following four vectors in (a) unit-vector notation, and in
(b) polar notation?
A: (2.00m)i + (3.00m)j
B: 4.00 m at 65o
C: (-4.00m)i – (6.00m)j
D: 5.00m at -235o