Question

The resultant of vectors A and B and is perpendicular to A and has the magnitude 24 units. If the sum of
magnitudes of A and B is 32 units, then their individual values may be

Answer 1

Answer on Question#55608 - Physics / Mechanics | Relativity

The resultant of vectors A and B and is perpendicular to A and has the magnitude 24 units. If the sum of magnitudes of A and B is 32 units, then their individual values may be

Solution

$\vec{\mathrm{A}} + \vec{\mathrm{B}}$ is perpendicular to $\vec{\mathrm{A}}$ so we have right-angled triangle. Now use Pythagoras' theorem:

$$(\vec{\mathrm{B}})^2 = (\vec{\mathrm{A}})^2 + (\vec{\mathrm{A}} + \vec{\mathrm{B}})^2,$$

and consider $(\vec{\mathrm{A}})^2 = |\mathrm{A}|^2$, $|\vec{\mathrm{A}} + \vec{\mathrm{B}}| = 24$, $|\mathrm{A}| + |\mathrm{B}| = 32$:

$$|B|^2 = (32 - |B|)^2 + 24^2 \rightarrow |B| = 25, |A| = 32 - 25 = 7.$$

Answer: $|B| = 25$, $|\mathrm{A}| = 7$

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