Question

A vector A makes an angle of 20 degree and vector B makes an angle of 110 degree with the x-axis. The magnitudes of these vectors are 3 m and 4 m 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 = 20°
Angle made by vector B = 110°
Angle between vector A and vector B = 110° - 20° = 90°

As given in question,
Magnitude of vector A , |A| = 3 m
Magnitude of vector B , |B| = 4 m
Resultant will be , R = √(A² + B²+2AB cosΘ) = 5 m

Let T be the angle between R vector and A vector.
T = tan⁻¹[(4sin90°)/(3 + 4cos90°)] = tan⁻1(4/3) = 53°

So, the resultant vector makes angle = (53° + 20°) = 73°
And also , 73° with respect to x-axis.

Hope it helps!

Answer 2

HEY!!

______________________________

⚫The angle between A and B will be 110-20 =90°

⚫The resultant will be (as cos90 = 0)

R = [A^2 + B^2]^1/2

R = [3^2 + 4^2^1/2= 25 
so,
R = 5 m

✔And it will be directed at an angle of 45 degrees