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If a and b are non-collinear vectors, then the value of for which the vectors u =( -2) a + b and v =(2+3 ) a -3 b are collinear is :

Options

  1. A3 2
  2. B2 3
  3. C- 3 2
  4. D- 2 3

Correct answer

B. 2 3

Step-by-step solution

Since, u and v are collinear, therefore aligned & u + v =0 & [k( -2)+2+3 ] a +(k-3) b =0 aligned Since a and b are non-collinear, then for some constant m and n , m a +n b =0 m=0, n=0 Hence from equation (i) aligned & k-3=0 k=3 & And k( -2)+2+3 =0 & 3( -2)+2+3 =0 = 2 3 aligned

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