Q.

Find A+B and A-B in the diagram shown in figure. Given A=4 units and B=3 units.

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30and13

37and10

37and13

13and37

answer is C.

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Detailed Solution

Addition R=A2+B2+2ABcosθ=16+9+2×4×3cos60°=37 units tanα=BsinθA+Bcosθ =3sin60°4+3cos60°=0.472 α=tan-1(0.472)=25.3° Thus, resultant of A and B is 37 units at angle 25.3° from A in the direction shown in figure Subtraction S=A2+B2-2ABcosθ=16+9-2×4×3cos60°=13 units And tanα=BsinθA-Bcosθ=3sin60°4-3cos60°=1.04 α=tan-1(1.04)=46.1° Thus, A-B is 13 units at 46.1° from A in the direction shown in figure

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