Ratios of Distances between Centroid, Circumcenter, Incenter and Orthocenter of Triangle
In Δ ABC , AB...
Question
In ΔABC,−−→AB=^i+3^j−2^k,−−→AC=3^i−^j−2^k. If the bisector of ∠BAC meets BC at D and G is the centroid of ΔABC, then |−−→GD|=
A
1
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B
13
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C
23
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D
2
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Solution
The correct option is A1 |−−→AB|=|−−→AC|=√14 ⇒ΔABC is isosceles. So, the bisector of ∠BAC coincide with the median through A. −−→AD=12(−−→AB+−−→AC)=2^i+^j−2^k |−−→AD|=3 Since, centroid divides the median in the ratio 2:1, we have 3|−−→GD|=|−−→AD|⇒|−−→GD|=1