More practice questions

4. Q4. A has magnitude 3 units and points north. Write, as a multiple of A, a vector of magnitude 12 units pointing south.

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   It is 4 times as long and opposite in direction, so it is −4A.

5. Q5. A is 3 units east and B is 4 units north. Find the magnitude of 2(A + B) and of 2A + 2B.

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   A + B has magnitude √(3^² + 4^²) = 5 units, so 2(A + B) has magnitude 10 units. 2A + 2B is 6 units east plus 8 units north, magnitude √(36 + 64) = 10 units: the same, as λ(A + B) = λA + λB says.

6. Q6. A particle has velocity v. What is its momentum if its mass is 3 kg, and what are the dimensions of the result?

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   p = (3 kg)v: along v, with magnitude 3v in kg m s^⁻¹ if v is in m s^⁻¹. Its dimensions are [M][L T^⁻¹] = [M L T^⁻¹], those of momentum.