Question

A\((3,5,-4)\), B\((-5,-5,-2)\), C\((-1,1,2)\) are the vertices of a triangle. \(P\) is a point on \(AB\) and \(CP\) is an angle bisector of \(\triangle ABC\). \(G\) is the centroid of the triangle \(ABC\). If the point which divides \(GP\) in the ratio \(1:3\) is \((\alpha,\beta,\gamma)\), then \(\alpha+\beta-\gamma=\)

• A. \(0\)
• B. \(1\)
• C. \(5\)
• D. \(3\)

Hint:

Use the Angle Bisector Theorem to locate the point on the opposite side. Then apply the section formula and the centroid formula successively.

Answer 1

The Correct Option is B