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Discussion Response Post to: vectors

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Titun (1467)

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The magnitude of resultant R of two vectors P & Q acting at an angle of

, is given by,

R² = P² + Q² + 2PQcos

Now, R² will be maximum when cos

= 1 i.e R² = (P+Q)²

Therefore, the maximim magnitude of R is (P+Q)

Again, R² will be minimum when cos

= -1 i.e R² = (P-Q) ²

Therefore, the minimum magnitude of R is l P - Q l

Now, by the conditions of the given problem,

magnitude of R _MAX= n . magnitude of R_MIN

i.e P + Q = n . l P - Q l

Assuming, P

Q, l P - Q l = P - Q

So, P+Q = nP - nQ i.e P = Q (1+n) / (n-1) ....... eqn. (1)

If the two vectors P & Q act at an angle of

the magnitude of resultant is (P+Q)/2

(P+Q)² / 4 = P² + Q² + 2PQ cos

Using eqn. (1) we have,

n² / (n-1) = (n+1)² / (n-1)² + 1 + 2(n+1) / (n-1) cos

.................. eqn (2)

If we assume that Q

P, we come to the same equation (2)

Hence from equation (2), find cos

in terms of n

Cheers !!!

You never know what is enough till you know what is more than enough. Titun

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