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If resultant of two vectors a & b is shown in the figure is ✓7b. The value of a/b.

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Asked by brijk456 1st August 2019, 10:00 AM
Answered by Expert
Answer:

Let x-axis of cartesian coord system is along the direction of  a .
 
Then we have  a = a i  ;  b = (b/2) i + (√3b/2)j
 
then resultant vector = [ a + (b/2) ] i + (√3b/2)j 
 
square of magnitude of resultant vector  = [ a + (b/2) ]2 + (3/4)b2 = 7 b2 (given)  
 
Hence,  we get from above equation,      a2 + ab = 6 b2  ..................(1)
 
dividing eqn.(1) by a2 ,  1 + (b/a)  = 6 (b/a)2  ....................(2)
 
put (b/a) - x in eqn.(2), we get,   6x2 -x -1 = (2x-1)(3x+1) = 0    or  x = b/a = 1/2
 
Answered by Expert 1st August 2019, 3:10 PM
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