A) \[2i+3j+k\]
B) \[2i+3j-k\]
C) \[2i-3j-k\]
D) \[-2i-3j-k\]
E) \[2i-3j+k\]
Correct Answer: A
Solution :
Given, the position vector of vertex A \[=2i+6j+4k\]and centroid of\[\Delta ABC\] \[=2i+4j+2k.\] We know that the median AM of\[\Delta ABC\]divided by centroid G, in the ratio\[2:1\]. Then, by section formula \[(2,4,2)=\left\{ \frac{2x+2}{2+1},\frac{2y+6}{2+1},\frac{2z+4}{2+1} \right\}\] On comparing, \[\Rightarrow \] \[2x+2=6\] \[\Rightarrow \] \[x=2\] \[\Rightarrow \] \[2y+6=12\] \[\Rightarrow \] \[y=3\] \[\Rightarrow \] \[22+4=6\] \[\Rightarrow \] \[z=1\] So, the position vector of M i.e., midpoint of BC is \[=2i+3j+k\]You need to login to perform this action.
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