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Question : 3 of 120
Marks:
+1,
-0
Solution:
Concept: - If two points A and B have position vectors and respectively, then the vector =−
- For two vectors and at an angle θ to each other:
- Dot Product is defined as: .=||||cosθ
- Resultant Vector is equal +.
- Work: The work (W) done by a force () in moving (displacing) an object along a vector is given by: W=.=||||cosθ
Calculation: Let's say that the forces acting on the particle are
=3+2+5 and
=2+−3 ∴The resulting force acting on the particle will be
=+ ⇒
=(3+2+5)+(2+−3) ⇒
=5+3+2.
Since the particle is moved from
2+2−3 to the point
4−3+7, the displacement vector
will be:
=(4−3+7)−(2+−3) ⇒
=2−2+10 And finally, the work done W will be:
W=.=(5+3+2).(2−2+10) ⇒
W=(5)(2)+(3)(−2)+(2)(10) ⇒
W=10−6+20=24‌units
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