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Vector addition and subtraction Knowledge-Based Practice

Physics · Introduction to Physics · Physics · Math Tools for Physics

5 Physics practice questions on Vector addition and subtraction. Questions that assess core concepts and understanding.

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Questions

  1. 1.

    Two vectors A⃗\vec{A} and B⃗\vec{B} have magnitudes of 9 units and 4 units, respectively. What are the minimum and maximum possible magnitudes of their resultant vector R⃗=A⃗+B⃗\vec{R} = \vec{A} + \vec{B}?

    • A) 4 units and 9 units
    • B) 5 units and 13 units
    • C) 0 units and 13 units
    • D) 5 units and 97\sqrt{97} units
  2. 2.

    Under what condition does the vector sum of two non-zero vectors u⃗\vec{u} and v⃗\vec{v} have the same magnitude as their vector difference, such that ∣u⃗+v⃗∣=∣u⃗−v⃗∣|\vec{u} + \vec{v}| = |\vec{u} - \vec{v}|?

    • A) The vectors u⃗\vec{u} and v⃗\vec{v} are perpendicular to each other.
    • B) The vectors u⃗\vec{u} and v⃗\vec{v} are parallel and point in the same direction.
    • C) The vectors u⃗\vec{u} and v⃗\vec{v} are antiparallel and point in opposite directions.
    • D) The vectors u⃗\vec{u} and v⃗\vec{v} have equal magnitudes regardless of orientation.
  3. 3.

    Three vectors satisfy the relationship A⃗+B⃗+C⃗=0⃗\vec{A} + \vec{B} + \vec{C} = \vec{0}. If A⃗=(4ı^−7ȷ^) m\vec{A} = (4\hat{\imath} - 7\hat{\jmath})\text{ m} and B⃗=(−9ı^+3ȷ^) m\vec{B} = (-9\hat{\imath} + 3\hat{\jmath})\text{ m}, which vector represents C⃗\vec{C}?

    • A) (−5ı^−4ȷ^) m(-5\hat{\imath} - 4\hat{\jmath})\text{ m}
    • B) (5ı^+4ȷ^) m(5\hat{\imath} + 4\hat{\jmath})\text{ m}
    • C) (−13ı^+10ȷ^) m(-13\hat{\imath} + 10\hat{\jmath})\text{ m}
    • D) (5ı^−10ȷ^) m(5\hat{\imath} - 10\hat{\jmath})\text{ m}
  4. 4.

    Given the vectors A⃗=(5ı^+2ȷ^) m\vec{A} = (5\hat{\imath} + 2\hat{\jmath})\text{ m} and B⃗=(1ı^−6ȷ^) m\vec{B} = (1\hat{\imath} - 6\hat{\jmath})\text{ m}, what is the resultant vector R⃗=2A⃗−3B⃗\vec{R} = 2\vec{A} - 3\vec{B}?

    • A) (13ı^−14ȷ^) m(13\hat{\imath} - 14\hat{\jmath})\text{ m}
    • B) (7ı^−14ȷ^) m(7\hat{\imath} - 14\hat{\jmath})\text{ m}
    • C) (13ı^+22ȷ^) m(13\hat{\imath} + 22\hat{\jmath})\text{ m}
    • D) (7ı^+22ȷ^) m(7\hat{\imath} + 22\hat{\jmath})\text{ m}
  5. 5.

    Two vectors in the xy-plane are given by A⃗=(6ı^−2ȷ^) m\vec{A} = (6\hat{\imath} - 2\hat{\jmath})\text{ m} and B⃗=(−2ı^+4ȷ^) m\vec{B} = (-2\hat{\imath} + 4\hat{\jmath})\text{ m}. What is the magnitude of the vector difference D⃗=A⃗−B⃗\vec{D} = \vec{A} - \vec{B}?

    • A) 25 m2\sqrt{5}\text{ m}
    • B) 213 m2\sqrt{13}\text{ m}
    • C) 8 m
    • D) 10 m

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