For what value of "a" , the magnitude of a vector A= 2i^+j^+ak^ should be 3?
Correct answer: D. Both A & B
- A. -2
- B. 2
- C. 4
- D. Both A & B
Explanation
The magnitude is |A| = √(2² + 1² + a²) = √(5 + a²). Setting this equal to 3 gives 5 + a² = 9, so a² = 4 and a = ±2. Therefore both -2 and 2 are possible; students who take only the positive square root choose 2 alone.
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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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