Q.1 (d) A force of magnitude 50 kN is acting at point A(2,3,4) m towards point B(6,−2,−3) m. Find the components of this force along X, Y and Z axis.
Best answer
Position vector: \(\vec{AB} = (6-2)\hat i + (-2-3)\hat j + (-3-4)\hat k = 4\hat i - 5\hat j - 7\hat k\) m
\(|AB| = \sqrt{16 + 25 + 49} = \sqrt{90} = 9.487\) m
Unit vector: \(\hat e_{AB} = \dfrac{4\hat i - 5\hat j - 7\hat k}{9.487} = 0.4216\hat i - 0.5270\hat j - 0.7379\hat k\)
Force: \(\vec F = 50\,\hat e_{AB} = 21.08\hat i - 26.35\hat j - 36.89\hat k\) kN
Answer: \(F_x = 21.08\) kN, \(F_y = -26.35\) kN, \(F_z = -36.89\) kN. (Check: \(\sqrt{21.08^2 + 26.35^2 + 36.89^2} = 50\) kN ✔)
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