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Let A ⃗ and B ⃗ be the two vectors of magnitude 10 unit each. If they are inclined to the X-axis at angles 30° and 60° respectively, find the resultant.

Let A ⃗ and B ⃗ be the two vectors of magnitude 10 unit each. If they are inclined to the X-axis at angles 30° and 60° respectively, find the resultant.

Grade:upto college level

3 Answers

Deepak Patra
askIITians Faculty 471 Points
9 years ago
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.
Pushpkar
20 Points
6 years ago
Let A and B be the two vectors of 10 unit each.A=B=10unit (Say both as A)Now angle between two vectors be 60-30=330So magn. of resultant is(A^2+B^2+2ABCos30°)^1/2 Here power of 1/2 means root.Since A=B then(A^2+A^2+2A.Acos30°)^1/2[2A^2+2A^2cos30]^1/2[2A^2(1+cos30)]^1/2[2A^2(2cos^2theta/2)]^1/2[4A^2cos^2.30/2]^1/2[4A^2cos^2.15]^1/22Acos152.10cos1520cos15° Answer
amit raj
19 Points
6 years ago
Angle between the vectors θ= 60°-30° =30°. Hence magnitude of the resultant = √(A²+B²+2ABcosθ) = √(10²+10²+2.10.10.cos30°) =√(200+200.√3/2) =10√(2+√3) = 19.32 unitsSince the vectors have equal magnitudes so the resultant bisects the angle θ between them. Angle between resultant and vector A =30°/2 =15°. So angle between resultant and X-axis =15°+30° =45°.

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