The unit vector in the direction of vector A = 2 i^ -2j^ + k^ is_______________?
Correct answer: C. (2i^ - 2j^ +k^)/3
- A. 2i^ - 2j^ + k^
- B. (2i^ - 2j^ +k^)/9
- C. (2i^ - 2j^ +k^)/3
- D. (2i^ - 2j^ +k^)/5
Explanation
The magnitude of A = 2i - 2j + k is sqrt((2)² + (-2)² + (1)²) = sqrt9 = 3. Dividing the vector by its magnitude gives the unit vector (2i - 2j + k)/3. Option b incorrectly divides by 9, which is the squared magnitude rather than the magnitude.
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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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