Question

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

Concept of Physics - 1 , HC VERMA , Chapter - "Physics and Mathematics"

Answer 1

Thanks for asking the question!

SOLUTION::

Please see figure to understand the solution more nicely.

Angle made by vector A = 30°
Angle made by vector B = 60°
Angle between vector A and vector B = 60° - 30° = 30°

As given in question,
Magnitude of vector A , |A| = 3 unit
Magnitude of vector B , |B| = 4 unit
Resultant will be , R = √(A² + B²+2AB cosΘ) = √(10² + 10²+2.10.10cos30°)
                                   = 19.3 unit 

Let T be the angle between R vector and A vector.
T = tan⁻¹[(10sin30°)/(10 + 10cos30°)] = tan⁻1[(1)/(2+√3)] = tan⁻¹(0.26795) 
                                                                                             = 15°

So, the resultant vector makes angle = (15° + 30°) = 45°
And also , 15° with respect to x-axis.

Hope it helps!

Answer 2

heya..



Let R be the magnitude of the resultant vector.

Rx = A cos30 + B cos60 = (10)(√3/2) + (10)(1/2) = 5(√3 + 1)

Ry = A sin30 + B sin60 = (10)(1/2) + (10)(√3/2) = 5(√3 + 1)

Angle between A and B is 300.

Therefore,

R = [(Rx)2 + (Ry)2 + 2(Rx)(Ry) cos30]1/2

=> R = 26.39 units

Angle made by the resultant with the X axis is,

tanΦ = Ry/Rx = 1

=> Φ = 450

hope helped..