Bear asked in Science & MathematicsPhysics · 4 weeks ago

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

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  • andrew
    Lv 7
    4 weeks 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

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