Question

Vector a points in the positive y direction and has a magnitude of 12 m. vector b has a magnitude of 33 m and points in the negative x direction. find the direction and the magnitude of

(a) a b
(b) a-b, and
(c) b-a.

Answer 1

To find the magnitude and direction of vectors a + b, a - b, and b - a, we add or subtract their magnitudes and use the same reference direction. For a + b, the magnitude is 45 m and the direction is 45 degrees north of the y-axis. For a - b, the magnitude is 21 m and the direction is 45 degrees north of the y-axis. For b - a, the magnitude is 21 m and the direction is 45 degrees south of the y-axis.

Step-by-step explanation:

To find the magnitude and direction of vector (a) a + b, we add the magnitudes of vectors a and b and use the direction of a as the reference. The magnitude of a is 12 m and the magnitude of b is 33 m. Adding these magnitudes gives us (12 + 33) m = 45 m. The direction of a + b can be determined by drawing a diagram or using trigonometry. Since a points in the positive y direction and b points in the negative x direction, the resultant vector a + b will be in the first quadrant but closer to the y-axis. Therefore, the direction of a + b is approximately 45 degrees north of the y-axis. Hence, the magnitude of vector a + b is 45 m and its direction is 45 degrees north of the y-axis.

For (b) a - b, we subtract the magnitudes of vectors a and b and use the same reference direction. The magnitude of a is 12 m and the magnitude of b is 33 m. Subtracting these magnitudes gives us (12 - 33) m = -21 m. Since the magnitude of a vector cannot be negative, we take the absolute value of -21 m, which is 21 m. The direction of a - b is the same as the direction of a + b, which is 45 degrees north of the y-axis. Hence, the magnitude of vector a - b is 21 m and its direction is 45 degrees north of the y-axis.

For (c) b - a, we subtract the magnitudes of vectors b and a and use the same reference direction. The magnitude of b is 33 m and the magnitude of a is 12 m. Subtracting these magnitudes gives us (33 - 12) m = 21 m. The direction of b - a is opposite to the direction of a + b, which is 45 degrees south of the y-axis. Hence, the magnitude of vector b - a is 21 m and its direction is 45 degrees south of the y-axis.