Physics-
General
Easy

Question

The simple sum of two co-initial vectors is 10 units. Their vector sum is 8 units. The resultant of the vectors is perpendicular to the smaller vector. The magnitudes of the two vectors are

  1. 2 units and 14 units  
  2. 4 units and 12 units  
  3. 6 units and 10 units  
  4. 8 units and 8 units  

The correct answer is: 6 units and 10 units


    P plus Q equals 16 (i)
    P to the power of 2 end exponent plus Q to the power of 2 end exponent plus 2 P Q c o s theta equals 64 (ii)
    tan90 degree equals fraction numerator Q s i n theta over denominator P plus Q c o s theta end fraction
    infinity equals fraction numerator Q s i n theta over denominator P plus Q c o s theta end fraction
    rightwards double arrow blank P plus Q c o s theta equals 0 blank or Q c o s theta equals negative P
    From Eq. (ii)
    P to the power of 2 end exponent plus Q to the power of 2 end exponent plus 2 P open parentheses negative P close parentheses equals 64 or Q to the power of 2 end exponent minus P to the power of 2 end exponent equals 64
    or open parentheses Q minus P close parentheses open parentheses Q plus P close parentheses equals 64
    or Q minus P equals fraction numerator 64 over denominator 16 end fraction equals 4(iii)
    Adding Eq. (i) and (iii), we get
    2 Q equals 20 or Q equals 10 units
    From (i), P plus 10 equals 16 or P equals 6 units

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