# Components Vector Sum Difference?

Vector A has magnitude of 6.0 at an angle of 50.0 o from the x-axis. Vector B has magnitude of 12.0 at an angle of -10.0 o from the x-axis. Let C=A+B. Let D=A-B. Let V=2*A-B.

What is the x-component of vector C?

What is the y-component of vector C?

What is the x-component of vector D?

What is the y-component of vector D?

What is the x-component of vector V?

What is the y-component of vector V?

### 1 Answer

- andrewLv 71 month ago
Vector A = 6.0 cos50° i + 6.0 sin50° j

Vector B = 12.0 cos(-10°) i + 12.0 sin(-10°) j

Vector B = 12.0 cos10° i - 12.0 sin10° j

Vector C = Vector A + Vector B

Vector C = (6.0 cos50° i + 6.0 sin50° j) + (12.0 cos10° i - 12.0 sin10° j)

Vector C = (6.0 cos50° + 12.0 cos10°) i + (6.0 sin50° - 12.0 sin10°) j

Vector D = Vector A - Vector B

Vector D = (6.0 cos50° i + 6.0 sin50° j) - (12.0 cos10° i - 12.0 sin10° j)

Vector D = (6.0 cos50° - 12.0 cos10°) i + (6.0 sin50° + 12.0 sin10°) j

Vector V = 2 × Vector A - Vector B

Vector V = 2 × (6.0 cos50° i + 6.0 sin50° j) - (12.0 cos10° i - 12.0 sin10° j)

Vector V = (12.0 cos50° - 12.0 cos10°) i + (12.0 sin50° + 12.0 sin10°) j

The answers:

The x-component of Vector C = 6.0 cos50° + 12.0 cos10° ≈ 15.7

The y-component of Vector C = 6.0 sin50° - 12.0 sin10° ≈ 2.5

The x-component of Vector D = 6.0 cos50° - 12.0 cos10° ≈ -8.0

The y-component of Vector D = 6.0 sin50° + 12.0 sin10° ≈ 6.7

The x-component of Vector D = 12.0 cos50° - 12.0 cos10° ≈ -4.1

The y-component of Vector D = 12.0 sin50° + 12.0 sin10° ≈ 11.3