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for internal and external division
Find the coordinate of the point P where the line through A(3, –4, –5) and B(2, –3, 1) crosses the plane passing through three points L(2, 2, 1), M(3, 0, 1) and N(4, –1, 0).
Also, find the ratio in which P divides the line segment AB.
If point C `(barc)` divides the segment joining the points A(`bara`) and B(`barb`) internally in the ratio m : n, then prove that `barc=(mbarb+nbara)/(m+n)`
If `bar p = hat i - 2 hat j + hat k and bar q = hat i + 4 hat j + 2 hat k` are position vector (P.V.) of points P and Q, find the position vector of the point R which divides segment PQ internally in the ratio 2:1
Show that the points A (1, –2, –8), B (5, 0, –2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.