Question

Three vectors a→, b→, and c→, each have a magnitude of 44.0 m
and lie in an *xy* plane. Their directions relative to the
positive direction of the *x* axis are 27.0 ˚, 192 ˚, and
315 ˚, respectively. What are **(a)** the magnitude
and **(b)** the angle of the vector a→+b→+c→ (relative
to the +*x* direction in the range of (-180°, 180°)), and
**(c)** the magnitude and **(d)** the
angle of a→-b→+c→ in the range of (-180°, 180°)? What are
**(e)** the magnitude and **(f)** the
angle (in the range of (-180°, 180°)) of a fourth vector d→ such
that (a→+b→)-(c→+d→)=0?

Answer #1

Three vectors a→, b→, and c→, each have a magnitude of 40.0 m
and lie in an xy plane. Their directions relative to the
positive direction of the x axis are 29.0 ˚, 191 ˚, and
315 ˚, respectively. What are (a) the magnitude
and (b) the angle of the vector a→+b→+c→ (relative
to the +x direction in the range of (-180°, 180°)), and
(c) the magnitude and (d) the
angle of a→-b→+c→ in the range of (-180°, 180°)? What...

Three vectors a→, b→, and c→, each have a magnitude of
53.0 m and lie in an xy plane. Their directions relative to the
positive direction of the x axis are 32.0 ˚, 191 ˚, and 311 ˚,
respectively. What are (a) the magnitude and (b) the angle of the
vector a→+b→+c→ (relative to the +x direction in the range of
(-180°, 180°)), and (c) the magnitude and (d) the angle of a→-b→+c→
in the range of (-180°, 180°)? What...

Three vectors a→, b→, and c→, each have a magnitude of 54.0 m
and lie in an xy plane. Their directions relative to the
positive direction of the x axis are 26.0 ˚, 191 ˚, and
314 ˚, respectively. What are (a) the magnitude
and (b) the angle of the vector a→+b→+c→ (relative
to the +x direction in the range of (-180°, 180°)), and
(c) the magnitude and (d) the
angle of a→-b→+c→ in the range of (-180°, 180°)? What...

Vectors A and B lie in an xy plane. Vector A has a magnitude of
8.1 and angle 144 degrees relative to +x direction; Vector B has
components Bx= -4.31 and By= -8.51. What are the angles between the
negative direction of the y axis and a) the direction of Vector A,
b) direction of the product of Vector AxB, and c) the direction of
Vector Ax(Vector B + 3.00k)?

The two vectors a and b in the figure have equal magnitude of 9
m and the angles are θ1 = 26° and θ2 = 95°. Find the x-component
and y-component of their vector sum r. What is the magnitude of
their vector sum r? Find the angle that their vector sum r makes
with the positive direction of the x-axis.

6.) Consider three force vectors F1 with magnitude 98 N and
direction 9◦ , F2 with magnitude 83 N and direction 133◦ , and F3
with magnitude 76 N and direction 285◦ . All direction angles θ are
measured from the positive x axis: counter-clockwise for θ > 0
and clockwise for θ < 0.
What is the direction of F as an angle between the limits of
−180◦ and +180◦ from the positive x axis with counterclockwise as
the...

1) The magnitude of vector A is 16, that of vector B is 22 and
that of vector C is 44. Vector A pointing north of west with an
angle of 32o above the -x axis, vector B is pointing
north of east with an angle of 19o clockwise (right) of
the +y axis and vector C is pointing south of west with an angle of
58o below the -x axis.
a) draw vectors A, B and C in the...

2. Two vectors, ~v1 and ~v2. ~v1 has a length of 12 and is
oriented at an angle θ1 = 30o relative to the positive x−axis. ~v2
has a length of 6 and is oriented at an angle θ2 = 0o relative to
the positive x−axis (it is aligned with the positive x−axis)
a. What are the magnitude and direction (angle) of the sum of
the two vectors ( 1+2 ~v = ~v1 + ~v2)?
b. What are the magnitude...

In the sum A→+B→=C→, vector A→ has a magnitude of 13.1 m and is
angled 43.6° counterclockwise from the +x direction, and
vector C→ has a magnitude of 15.4 m and is angled 15.9°
counterclockwise from the -x direction. What are
(a) the magnitude and (b) the
angle (relative to +x) of B→? State your angle as a
positive number.

In the sum A→+B→=C→, vector A→ has a magnitude of 13.9 m and is
angled 37.5° counterclockwise from the +x direction, and
vector C→ has a magnitude of 13.0 m and is angled 23.0°
counterclockwise from the -x direction. What are
(a) the magnitude and (b) the
angle (relative to +x) of B→? State your angle as a
positive number.

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