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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

Consider the points A( o ), B(3 i +f(t) j + k ) and C (2 i +f^ (t) j +2 k ) and another point D are coplanar for all t R

Options

  1. Aif D is ( i ) then f(x)=c e^ 2 x , c R
  2. Bif D is ( i ) then f(x)=c (2 x), c R
  3. Cif D is ( i + j ) then f(x)=2+c e^ 2 x , x R
  4. Dif D is ( i + j ) then f(x)=2+c (2 x), c R

Correct answer

C. if D is ( i + j ) then f(x)=2+c e^ 2 x , x R

Step-by-step solution

Four point A, B, C, D are coplanar if three vector A B , A C , A D are coplanar or STP of there vectors is 0 aligned & AB ( AC AD )=0 & | array ccc 1 & 0 & 0 3 & f(t) & 1 2 & f^ (t) & 2 array |=0 t R & f^ (t)=2 f(t) & f(t)=c e^ 2 t aligned Similarly for B ( i + j ) differential equation will be f^ (t)-2 f(t)=-4 On solving f(x)=2+c e^ 2 x , c R

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