Let A vector and B vector be the vectors of magnitude 10units each. If they are Inclined to the X- axis at angles 30 degree and 60 degree respectively, find the resultant
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Sol. Angle between A ⃗ and B ⃗ is θ = 60° - 30° = 30°
|A ⃗ | and |B ⃗ | = 10 unit
R = √(〖10〗^2+〖10〗^2+2.10.10.cos〖30°〗 ) = 19.3
Β be the angle between |R ⃗ | and |A ⃗ |
Β = tan^-1 ((10 sin〖30°〗)/( 10+10 cos〖30°〗 )) = tan -1 (1/(2+√3)) = tan^-1 (2.26795) = 15°
∴ Resultant makes 15° + 30° = 45° angle with x-axis.
|A ⃗ | and |B ⃗ | = 10 unit
R = √(〖10〗^2+〖10〗^2+2.10.10.cos〖30°〗 ) = 19.3
Β be the angle between |R ⃗ | and |A ⃗ |
Β = tan^-1 ((10 sin〖30°〗)/( 10+10 cos〖30°〗 )) = tan -1 (1/(2+√3)) = tan^-1 (2.26795) = 15°
∴ Resultant makes 15° + 30° = 45° angle with x-axis.
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