If A = 2i+j+2k then its magnitude is:
Correct answer: C. 3
- A. 9
- B. 5
- C. 3
- D. 1
Explanation
To calculate the magnitude of a vector, we can use the formula:|A| = √(Ax² + Ay² + Az²Where 'A' is the vector and Ax, Ay, and Az are the components of the vector in the x, y, and z directions, respectively.We have,-A = 2i + j + 2kLet's calculate the magnitude:|-A| = √(2)² + (1)² + (2)²= √ (4+1+4)= √(9)= 3Therefore, the magnitude of the vector -A is 3.
This question appeared on the ETEA MDCAT 2010 paper, which you can sit online with every answer explained.
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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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