Question

Two vectors P and Q are at an angle. Prove that the resultant of these vectors are given by:
R=(P²+Q²+2PQ COS)¹/²​

Answer 1

Answer:

its not the vector it is only the magnitude

Explanation:

let vector p = ai + bj and q = ci + dj ( here i, j are unit vectors along x and y axes respectively)

Resultant vector of p and q is vector addition of vectors p and q

so, the resultant vector r = p+q = (a+c)i + ( b+d)j

magnitude of vector r is [ (a+c)² + (b+d)² ]½

on simplifying, r² = (a²+b²) + (c²+d²) + 2(ac+bd) ......eq.1

we have dot product of vectors p and q as

p.q = |p|.|q|.cos(t) = ac + bd .....eq.2 ; where t is the angle between p and q

from equations 1 and 2, r² = |p|² + |q|² + 2|p|.|q|.cos(t)

So, r = ( p² + q² + 2pq cos(t) ) ½

HOPE THIS HELPS YOU...