Two vectors acting in the opposite directions have a resultant of 10 units. If they act at right angles to each other, then the resultant is 50 units. Calculate the magnitude of two vectors.
A
40,30
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B
50,40
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C
40,50
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D
30,40
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Solution
The correct options are A40,30 D30,40 Let →P&→Q are two vectors. Case 1: P>Q For opposite direction, P−Q=10 unit -------(1) For perpendicular direction, √P2+Q2=50 unit P2+Q2=502.....(2) From equation (1) and (2) (10+Q)2+Q2=502 2Q2+20Q+100=2500 2Q2+20Q=2400 Q2+10Q−1200=0 (Q+40)(Q−30)=0 Q=30 units (we cannot take negative sign because magnitude cannot be negative) So, from equation (1) P=10+Q =10+30 P=40 units Case 2: P<Q Simillarly, from equation 1 and 2 (Q−10)2+Q2=502 Then, Q=40 Units Then, P=Q−10 P=30 Units