question_answer

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     AIEEE  Solved  Paper-2005

A) the harmonic mean of a and b

B) equal to zero

C) the arithmetic mean of a and b

D) the geometric mean of a and b

Correct Answer: D

Solution :

If three vectors a, b and c are coplanar, then Since, the given points lies in a plane, then Applying Therefore, c is GM of a and b.