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दो सदिशों `vec(A)` व `vec(B)` के परिमाण क्रमशः 4 मात्रक व 3 मात्रक तथा इनके बीच कोण `60^(@)` है । ज्ञात कीजिये -
(i) `vec(A)+vec(B)` का परिमाण व दिशा
(ii) `vec(A)-vec(B)` का परिमाण व दिशा |

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(i) यदि `vec(R)=vec(A)+vec(B)` हो तो `vec(A)+vec(B)` का परिमाण
`R=sqrt(A^(2)+B^(2)+2ABcostheta)`
प्रश्नानुसार, `A=4` मात्रक, `B=3` मात्रक, `theta=60^(@)`
`:." "R=sqrt((4)^(2)+(3)^(2)+2xx4xx3xxcos60^(@))`
`=sqrt(16+9+12)" "(becausecos60^(@)=(1)/(2))`
`=sqrt(37)` मात्रक
यदि `vec(R)` व `vec(A)` के बीच कोण `alpha` हो तो
`tanalpha=(Bsintheta)/(A+Bcostheta)=(3sin60^(@))/(4+3cos60^(@))=(3(sqrt(3)//2))/(4+3(1//2))`
`=(3sqrt(3))/(11)=0.472`
`:." "alpha=tan^(-1)(0.472)=25.3^(@)`
(ii) यदि `vec(S)=vac(A)-vec(B)` हो तो `vec(A)-vec(B)` का परिमाण
`S=sqrt(A^(2)+B^(2)-2ABcostheta)`
`=sqrt((4)^(2)+(3)^(2)-2xx4xx3xxcos60^(@))`
`=sqrt(13)` मात्रक
यदि `vec(S)` व `vec(A)` के बीच कोण `alpha` हो तो
`tanalpha=(Bsintheta)/(A-Bcostheta)=(3sin60^(@))/(4-3cos60^(@))=(3sin60^(@))/(4-3cos60^(@))=(3(sqrt(3)//2))/(4-3(1//2))`
`=(3sqrt(3))/(5)=1.04`
`:." "alpha=tan^(-1)(1.04)=46.1^(@)`

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