Vector A with arrow is directed along the positive y-axis and has magnitude 9.0 units. Vector B with arrow is directed along the negative x-axis and has magnitude 4.0 unit.
(a) What are the magnitude and direction of A with arrow + B with arrow?
magnitude
Incorrect: Your answer is incorrect.
unit(s)
direction ° counterclockwise from the +x-axis
(b) What are the magnitude and direction of A with arrow − B with arrow?
magnitude unit(s)
direction ° counterclockwise from the +x-axis
(c) What are the x- and y-components of B with arrow − A with arrow?
x =
y =
With Arrow
A = 9i
B = -4
a. A+B = 9i + (-4) Q2.
A+B = sqrt(9^2+(-4^2) = 9.85 Units.
Tan Theta = 9/-4 = -2.25
Theta = -66.0 + 180 = 114o, CCW(Q2).
b. A-B = 9i - (-4) = 9i + 4
A-B = sqrt(9^2+4^2) = 9.85 Units.
Tan Theta = 9/4 = 2.25
Theta = 66o
c. B-A = -4 - 9i
X = -4
Y = -9
To solve this problem, we will use vector addition and subtraction.
(a) To find the magnitude and direction of A + B, we first need to find the components of vector A and vector B.
Vector A is directed along the positive y-axis, so its x-component is 0 and its y-component is 9.0 units.
Vector B is directed along the negative x-axis, so its x-component is -4.0 units and its y-component is 0.
Next, we add the components of A and B to get the components of A + B:
x-component of A + B = 0 + (-4.0) = -4.0 units
y-component of A + B = 9.0 + 0 = 9.0 units
The magnitude of A + B can be found using the Pythagorean theorem:
magnitude of A + B = sqrt((-4.0)^2 + 9.0^2) = sqrt(16.0 + 81.0) = sqrt(97.0) ≈ 9.85 units
The direction of A + B can be found using the arctan function:
direction of A + B = arctan(9.0 / -4.0) ≈ -66.8 degrees (counterclockwise from the +x-axis)
(b) To find the magnitude and direction of A - B, we subtract the components of vector B from vector A.
x-component of A - B = 0 - (-4.0) = 4.0 units
y-component of A - B = 9.0 - 0 = 9.0 units
The magnitude of A - B can be found using the Pythagorean theorem:
magnitude of A - B = sqrt(4.0^2 + 9.0^2) = sqrt(16.0 + 81.0) = sqrt(97.0) ≈ 9.85 units
The direction of A - B can be found using the arctan function:
direction of A - B = arctan(9.0 / 4.0) ≈ 64.5 degrees (counterclockwise from the +x-axis)
(c) To find the x- and y-components of B - A, we subtract the components of vector A from vector B.
x-component of B - A = -4.0 - 0 = -4.0 units
y-component of B - A = 0 - 9.0 = -9.0 units