Question

The resultant of two vectors P and Q is R. If the magnitude of Q is doubled, the new resultant becomes perpendicular to then the magnitude of Ris.​

Answer 1

Answer:

Step 1: Initial resultant between two vectors [Ref. Fig. 1]

Resultant of P and Q,

∣∣∣∣R∣∣∣∣2=∣∣∣∣P∣∣∣∣2+∣∣∣∣Q∣∣∣∣2+2∣∣∣∣P∣∣∣∣∣∣∣∣Q∣∣∣∣cosθ                            ....(1)

Step 2: Dot product between new resultant and P  [Ref. Fig. 2]

When Q is doubled, new resultant, R1 =P+2Q  becomes perpendicular to