Questions
190867 Mechanics and Thermodynamics Test 1 (chapters 1-6)
Multiple fill-in-the-blank
Here are two vectors: a→=(4.0m)i^−(3.0m)j^\vec{a}=(4.0m)\rm{\hat{i}} - (3.0m)\rm{\hat{j}} b→=(6.0m)i^+(8.0m)j^\vec{b}=(6.0m)\rm{\hat{i}} + (8.0m)\rm{\hat{j}} What are (a) the magnitude and (b) the angle (relative to i^\rm{\hat{i}}) of a→\vec{a} ? What are (c) the magnitude and (d) the angle of b→\vec{b} ? What are (e) the magnitude and (f) the angle of a→+b→\vec{a}+\vec{b} ? What are (g) the magnitude and (h) the angle of b→−a→\vec{b}-\vec{a} ? What are (i) the magnitude and (j) the angle of a→−b→\vec{a}-\vec{b} ? What is (k) the angle between the directions of b→−a→\vec{b}-\vec{a} and a→−b→\vec{a}-\vec{b} ? Please round your answers to zero decimal places. (a) the magnitude of a→\vec{a} = [Fill in the blank], m (b) the angle off a→\vec{a} = [Fill in the blank], o (c) the magnitude of b→\vec{b} = [Fill in the blank], m (d) the angle of b→\vec{b} = [Fill in the blank], o (e) the magnitude of a→+b→\vec{a}+\vec{b} = [Fill in the blank], m (f) the angle of a→+b→\vec{a}+\vec{b} = [Fill in the blank], o (g) the magnitude of b→−a→\vec{b}-\vec{a} = [Fill in the blank], m (h) the angle of b→−a→\vec{b}-\vec{a} = [Fill in the blank], o (i) the magnitude of a→−b→\vec{a}-\vec{b} = [Fill in the blank], m (j) the angle of a→−b→\vec{a}-\vec{b} = [Fill in the blank], o (k) the angle between b→−a→\vec{b}-\vec{a} and a→−b→\vec{a}-\vec{b} = [Fill in the blank], o

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Step-by-Step Analysis
We start by parsing the given vectors and computing the requested quantities step by step, then we evaluate how each proposed numeric value lines up with the correct results after rounding to zero decimal places.
a) Magnitude of a = (4, -3)
- Compute: sqrt(4^2 + (-3)^2) = sqrt(16 + 9) = sqrt(25) = 5.
- Among the options for (a), the value 5 is exactly correct. Other nearby values are not exact magnitudes; they do not match the true result.
b) Angle of a relative to i-hat (in degrees, measured from +x, positive counterclockwise)
- Angle = arctan(y/x) = arctan(-3/4) ≈ -36.87°. Rounding to zero decimals gives -37°.
- In the list, -37 is present and matches the rounded value. The exact -36.87 and -36.9 are the unrounded or closer representations, but the instruction asks for zero-decimal rounding, so -37 is the appropriate rounded answer.
c) Magnitude ......Login to view full explanationLog in for full answers
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