Question

Obtain the Expression for magnitude and direction for the resultant of two bectors making an angle between them​

Answer 1

Explanation:

Parallelogram law states that if two vectors are considered to be the adjacent sides of a Parallelogram, then the resultant of two vectors is given by the vector which is a diagonal passing through the point of contact of two vectors. In the figure → P P→ and → Q Q→ are two vectors.with magnitudes equal to length OA and OB respectively and making angle θ between them. Complete the parallelogram, OACB, Join diagonal OC , that makes angle α with vector → P P→. According to parallelogram law of vectors the resultant is represented by the diagonal passing through the point of contact of two vectors. To find the magnitude of resultant , produce a perpendicular CD to meet OA produced to D. From △ OCD, OC2 = OD2 +CD2 Now, → C D C→D = → A C s i n θ = → Q s i n θ A→Csinθ=Q→sinθ AD = → A C c o s θ = → Q c o s θ A→Ccosθ=Q→cosθ → O D = → O A + → A D = → P + → Q c o s θ O→D=O→A+A→D=P→+Q→cosθ Putting these values and representing resultant vector OC by → R R→, magnitude of the resultant is given by R2 = ( → P P→ + → Q Q→cosθ)2 + ( → Q Q→ sinθ)2 = → P 2 P→2 + → Q 2 Q→2 + 2 → P P→ → Q Q→cosθ In △ OCD, tan α α = C D O D CDOD= → Q s i n θ → P + → Q c o s θ Q→sinθP→+Q→cosθ Resultant acts in the direction making an angle α = tan-1 ( → Q s i n θ → P + → Q c o s θ ) (Q→sinθP→+Q→cosθ) with direction of vector P. Read more on Sarthaks.com - https://www.sarthaks.com/977581/derive-the-expression-for-resultant-magnitude-and-direction-of-two-force-acting-at-point