question_answer

If a, b, c are different real numbers and \[a\,\,\hat{i}+b\,\,\hat{j}+c\,\,\hat{k},\]\[b\,\,\hat{i}+c\,\,\hat{j}+a\,\,\hat{k}\] and \[c\,\,\hat{i}+a\,\,\hat{j}+b\,\,\hat{k}\]are position vectors of three non-collinear points, then

A)  centroid of \[\Delta ABC\] is s\[\frac{a+b+c}{3}\,(\hat{i}+\hat{j}+\hat{k})\]

B)  \[(\hat{i}+\hat{j}+\hat{k})\] is not really inclined to three vectors

C)  triangle ABC is a scalene triangle

D)  perpendicular from the origin to the plane of the triangle does not meet it at the centroid