Question

Prove that the Triangle Law of vector addition analytically

Answer 1

Answer:

Triangle law of Vector addition

Let vector A and B be represented on the two sides of a triangle .(refer figure)

drop a perpendicular RS to PR

SP^2 = PR^2+SR^2

or, sp^2 = (A+QR)^2 + SR^2

In Triangle sqr

SR/B = sinQ

SR = BsinQ

similarly ,

QR/B = cosQ

QR = BcosQ

substituting in main equation

sp^2 = (A+BcosQ)^2 + (BsinQ)^2

R^2 = A^2 + 2ABCosQ + B^2CosQ^2 + B^2sinQ^2

R = √A^2 + B^2 + 2ABCosQ

tan P = sr/PR

or, tan P = BsinQ/(A+BcosQ)

ie, direction