At what angle should two force vectors of 5N and 12 N be added to get a resultant vector of 13 N?
Question
At what angle should two force vectors of 5N and 12 N be added to get a resultant vector of 13 N?
Solution
To find the angle at which the two vectors should be added, we can use the law of cosines. The law of cosines states that for any triangle with sides of lengths a, b, and c, and an angle γ between a and b, the following equation holds:
c² = a² + b² - 2ab cos(γ)
In this case, the sides of the triangle are the magnitudes of the two vectors (5N and 12N) and the resultant vector (13N). We can rearrange the law of cosines to solve for the angle γ:
cos(γ) = (a² + b² - c²) / (2ab)
Substituting the given values:
cos(γ) = (5² + 12² - 13²) / (2 * 5 * 12)
cos(γ) = (25 + 144 - 169) / 120
cos(γ) = 0
Therefore, γ = cos⁻¹(0) = 90 degrees.
So, the two force vectors of 5N and 12N should be added at an angle of 90 degrees to get a resultant vector of 13N.
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