Question

Two vectors P and Q have magnitudes 3 units and 4 units respectively. Ř is the
resultant of P and Q. Find the magnitude and direction of Ř when the angle theta
between P and Q is 30°.​

Answer 1

Answer:

R = _/P^2 +Q^2 + 2PQ COS@

R= _/3^2 + 4^2 + 2 (4)(3) COS 30°

R= _/9 + 16 + 24 COS 30°

R= _/25 + 24 (_/3 / 2)

R = _/ 25 + 12_/3

R= _/25 + _/ 12 _/(_/3)

R= 9.55

R= 10(approx.)

NOW ,

TAN beeta = Q SIN @ / P + Q COS@

= 4 SIN 30 / 3 + 4 COS 30

= 4 (1/2) / 3+ 4 (_/3 / 2)

= 2./ 3 + 2_/3

= 2 / (3_/3 +2)/_/3

= 2 / ( 9 +2 _/3)

therefore ,beeta = TAN^-1 [ 2/ (9+ 2_/3) ]

you can solve it further if you want

just rationalize 9 + 2_/3

pls mark it as brainlist