Question

Vector A has a magnitude of 8 units and makes an angle of 45 degrees with the x-axis. Vector B has the same magnitude of 8 units and is directed along the negative x-axis. Find:

A) Magnitude and direction of A + B
B) Magnitude and direction of A - B
a) A) 8√2, 45 degrees; B) 8√2, 225 degrees
b) A) 8, 45 degrees; B) 8, 225 degrees
c) A) 8√2, 135 degrees; B) 8√2, 225 degrees
d) A) 8, 135 degrees; B) 8, 225 degrees

Answer 1

To find the magnitude and direction of vector A + B and A - B, you can add or subtract their x-components and y-components separately. The magnitude can be found using the Pythagorean theorem and the direction can be found using trigonometry.

Step-by-step explanation:

To find the magnitude and direction of vector A + B, we can add the x-components and y-components separately. The x-component of A + B can be found by adding the x-component of A and the x-component of B, and the y-component of A + B can be found by adding the y-component of A and the y-component of B. The magnitude of A + B can be found using the Pythagorean theorem, and the direction can be found using trigonometry. To find the magnitude and direction of A - B, we follow the same process, but subtract the x-components and y-components.

For A + B:

Ax + Bx = 8 cos(45°) - 8 cos(180°) = 8 √2

Ay + By = 8 sin(45°) - 8 sin(180°) = 0

Magnitude of A + B = √((8 √2)^2 + 0^2) = 8 √2

Direction of A + B = tan^(-1)(0 / (8 √2)) = 0°

For A - B:

Ax - Bx = 8 cos(45°) - (-8 cos(180°)) = 8 √2

Ay - By = 8 sin(45°) - (-8 sin(180°)) = 0

Magnitude of A - B = √((8 √2)^2 + 0^2) = 8 √2

Direction of A - B = tan^(-1)(0 / (8 √2)) = 0°