determine the magnitude and direction of the resultant for a combination of the vectors A: 10.1m, 60 degrees B: 7.3m, 275 degrees

5.87 m, 75.5°

Explanation:

Let's say C is the resultant vector.

The x component is the sum of the x components of A and B.

Cx = Ax + Bx

Cx = 10.1 cos 60° + 7.3 cos 275°

Cx = 5.69

The y component is the sum of the y components of A and B.

Cy = Ay + By

Cy = 10.1 sin 60° + 7.3 sin 275°

Cy = 1.47

The magnitude is found with Pythagorean theorem, and the angle is found with trigonometry.

C² = Cx² + Cy²

C² = 5.69² + 1.47²

C = 5.87

θ = atan (Cy / Cx)

θ = atan (5.69 / 1.47)

θ = 75.5°