Two vectors of magnitude 10m and 20m have an angle 30o between them. The component of shorter vector parallel to the longer vector will be:
Correct answer: B. 8.66 m
- A. 5 m
- B. 8.66 m
- C. 10 m
- D. 17.32 m
Explanation
Taking |A| = 10m and |B| = 20m, with an angle of 30o between them.We are going to find the projection of A along B (of shorter along longer).Since one angle is given, the vector can have two components orthogonally. As a convention, we can take the longer vector along x-axis and join the tails of two vectors such that the given angle is reached.Projection of A along B = AcosθAcosθ = (10)cos30oAcosθ = (10)(0.866) m = 8.66 m
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