I. Two non-zero, non-collinear vectors are linearly independent. II. Any three coplanar vectors are linearly…

I. Two non-zero, non-collinear vectors are linearly independent. II. Any three coplanar vectors are linearly dependent. Which of the above statements is/are true?
  1. Only I
  2. Only II
  3. Both I and II
  4. Neither I nor II

Solution

I : It is true that non-zero, non-collinear vectors are linearly independent. II : It is also true that any three coplanar vectors are linearly dependent. $\therefore$ Both I and II are true.

Asked in: AP EAMCET 2005

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