If |F1| =3cm and |F2| =4cm, F1 is making an angle of 30o and F2 is making an angle of 120o with the x-axis, then their scalar product is:
Correct answer: A. 0 cm2
- A. 0 cm2
- B. 6 cm2
- C. 10.39 cm2
- D. 12 cm2
Explanation
The following is the solution: If we take a circle centred at origin with radius 3, components of F1 will be, F1=< 3Cos30°, 3Sin30° >=< 3√3/2, 3/2 > Similarly components of F2 will be, F2=< 4Cos120°, 4Sin120° >=< −2, 2√3 > F1∙F2=3√3/2 x −2 + 3/2 x 2√3 F1∙F2= −3√3+ 3√3 =0 The other way we can find scalar product of two vectors or forces is by, F1∙F2=||F1|| x ||F2|| x Cosθ F1∙F2=3 x 4 x Cos90°=0
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Vectors have magnitude and direction, unlike scalars, and are combined by head-to-tail or parallelogram methods. Work covers rectangular components, equilibrium when the resultant force is zero, the scalar product for work and projections, and the vector product for torque and cross-product direction using the right-hand rule.
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