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Question:

A slob is subjected to two forces →F1 and →F2 of same magnitude F as shown in the figure. Force →F2 is in XY-plane while force →F1 acts along z-axis at the point (2→i+3→j). The moment of these forces about point O will be :

(3^i+2^j+3^k)F

(3^i+2^j−k)F

(3^i−2^j+3^k)F

(3^i−2^j−k)F

Solution:

→F1=F^(k)
→r1=2→i+3→j
→τF1=→r1×→F1=(2→i+3→j)×F^(k)=3F→i−2F→j
Torque for F2 force
→F2=F(cosθ→i+sinθ→j)
→r2=2→i+3→j
→τF2=→r2×→F2=(2→i+3→j)×F(cosθ→i+sinθ→j)=−3Fsinθ→i+2Fcosθ→j
→τnet=→τF1+→τF2=3F→i−2F→j−3Fsinθ→i+2Fcosθ→j=(3F−3Fsinθ)→i+(−2F+2Fcosθ)→j
If θ=0, then →F2=F→i
→τF2=→r2×→F2=(2→i+3→j)×F→i=3F→k
→τnet=3F→i−2F→j+3F→k