Question

The resultant of two vectors P and Q is R. If the magnitude of Q doubled, the new resultant
become perpendicular to vector P. Then the magnitude of R is
1) P+Q
2) Q
3)P
4)P+Q/2​

Answer 1

Answer:

2) Q

Step-by-step explanation:

@ : angle b/w P & Q

¢ : angle b/w P & R

if Q' = 2Q then ¢ = 90°

but...

tan ¢ = Q sin @ / P + Q cos @

tan 90° = Q' sin @ / P + Q' cos @

∞ = 2Q sin @ / P + 2Q cos @

i,e P + 2Q cos @ = 0

cos @ = - P/2Q

now.....

R^2 = P^2 + Q^2 + 2PQ cos @

R^2 = P^2 + Q^2 + 2PQ (-P/2Q)

R^2 = P^2 + Q^2 - P^2

R^2 = Q^2

R = Q