If A is 3i + 4j, its magnitude is
Correct answer: B. 5
- A. 7
- B. 5
- C. 12
- D. 25
Explanation
The magnitude is the square root of the sum of the squares of the components, so the square root of (9 plus 16), which is the square root of 25, that is 5. Adding the components to get 7 ignores that they are perpendicular. The value 25 is the square of the magnitude, quoted before taking the root.
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About Rectangular Components
A vector is resolved into perpendicular horizontal and vertical components using trigonometric relations, usually as Ax = A cos θ and Ay = A sin θ when θ is measured from the horizontal. Questions involve signs in different quadrants, reconstructing a resultant from components, and using components to analyse equilibrium.
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