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Let a,b \; and\, \; c be distinct non­-negative numbers. If the vectors a\hat{i}+a\hat{j}+c\hat{k},\; \hat{i}+\hat{k}\; and\; c\hat{i}+c\hat{j}+b\hat{k}  lie in a plane, then c is

  • Option 1)

    the arithmetic mean of a\; \; and\; \; b

  • Option 2)

    the geometric mean of  a\; \; and\; \; b

  • Option 3)

    the harmonic mean of a\; \; and\; \; b

  • Option 4)

    equal to zero

 

The value of a, for which the points A,B,C with position  vectors 2\hat{i}-\hat{j}+\hat{k},\; \; \hat{i}-3\hat{j}-5\hat{k}\; \; and\; \; a\hat{i}-3\hat{j}+\hat{k}  respectively are the vertices of a right angled triangle at c are

  • Option 1)

    2 and 1

  • Option 2)

    –2 and –1

  • Option 3)

    –2 and 1

  • Option 4)

    2 and –1

 
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