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
Correct Answer: A
Solution :
Given, position vectors of a triangle are \[a\hat{i}+b\hat{j}+c\hat{k},\,\,b\hat{i}+c\hat{j}+a\hat{k}\] and \[c\hat{i}+a\hat{j}+b\hat{k}\] Then, centroid of triangle is \[\frac{a+b+c}{3}\,(\hat{i}+\hat{j}+\hat{k})\]You need to login to perform this action.
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