A vector has component along the x-axis equal to 25 unit and along the y-axis equal to 60 unit. Find the magnitude and direction of the vector.
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Answer :-
- |R| = 65 units
- θ = 67.38°
Explanation :-
# Given :-
- x = 25 units
- y = 60 units
# Solution :-
Let R be the supposed vector such that -
R = xi + yj
Resultant magnitude of vector R is given by -
|R| = √(x² + y²)
|R| = √(25² + 60²)
|R| = √(625 + 3600)
|R| = √(4225)
|R| = 65 units
Direction of vector R is given as -
θ = arctan(y / x)
θ = arctan(60 / 25)
θ = arctan(2.4)
θ = 67.38°
Therefore, required vector has magnitude 65 units & it makes angle of 67.38° with X-axis.
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