Three vectors of equal magnitudes (let P) are lying in a plane such that respective angle between one another is 45?, then the magnitude of these resultants would be

Question

Three vectors of equal magnitudes (let P) are lying in a plane such that respective angle between one another is 45?, then the magnitude of these resultants would be (A)  √3 (P+1)  (B)  √2P2+3  (C) zero (D)  P(√2+1)

Tardigrade Admin · Accepted Answer

Let the vectors are OA , OB and OC shown below.
Given that, OA = OB = OC = P Clearly, the resultant ofOA and OC willbe in the direction of OB. The magnitude of OA + OC

= 2 P cos 45^{\circ} = P 2

Now, magnitude of resultant vector along OB is

P + P 2 = P (2 + 1)

Q. Three vectors of equal magnitudes (let P) are lying in a plane such that respective angle between one another is 45?, then the magnitude of these resultants would be

$3 (P + 1)$

$2 P^{2} + 3$

zero

$P (2 + 1)$

Let the vectors are OA , OB and OC shown below.
Given that, OA = OB = OC = P Clearly, the resultant ofOA and OC willbe in the direction of OB. The magnitude of OA + OC $= 2 P cos 45^{\circ} = P 2$ Now, magnitude of resultant vector along OB is $P + P 2 = P (2 + 1)$

Q. Three vectors of equal magnitudes (let P) are lying in a plane such that respective angle between one another is 45?, then the magnitude of these resultants would be

3(P+1)​

2P2+3​

zero

P(2​+1)

Let the vectors are OA , OB and OC shown below.Given that, OA = OB = OC = P Clearly, the resultant ofOA and OC willbe in the direction of OB. The magnitude of OA + OC =2Pcos45∘=P2​ Now, magnitude of resultant vector along OB is P+P2​=P(2​+1)

$3 (P + 1)$

$2 P^{2} + 3$

$P (2 + 1)$

Let the vectors are OA , OB and OC shown below.
Given that, OA = OB = OC = P Clearly, the resultant ofOA and OC willbe in the direction of OB. The magnitude of OA + OC $= 2 P cos 45^{\circ} = P 2$ Now, magnitude of resultant vector along OB is $P + P 2 = P (2 + 1)$