Search any question & find its solution
Question:
Answered & Verified by Expert
Let $A=(1,2,0), B=(2,0,-1), C=(0,-2,3)$ and $D=(-1,2,-3)$ be four points in the space. Let $\mathrm{G}_1$ be the centroid of triangle $A B C$ and $G_2$ be the centroid of tetrahedron ABCD. If $P$ divides $G_1 G_2$ in the ratio $4: 3$ internally then $\mathrm{P}=$
Options:
Solution:
1899 Upvotes
Verified Answer
The correct answer is:
$\left(\frac{5}{7}, \frac{2}{7}, \frac{1}{7}\right)$
Given points are $\mathrm{A}=(1,2,0), \mathrm{B}=(2,0,-1)$, $\mathrm{C}=(0,-2,3)$ and $\mathrm{D}=(-1,2,-3)$
Here $\mathrm{G}_1=(1,0,2 / 3)$ and $\mathrm{G}_2=(1 / 2,1 / 2,-1 / 4)$
Now $P$ divides $G_1 G_2$ in the ratio $4: 3$ internally
So, $\mathrm{P}=(5 / 7,2 / 7,1 / 7)$
Here $\mathrm{G}_1=(1,0,2 / 3)$ and $\mathrm{G}_2=(1 / 2,1 / 2,-1 / 4)$
Now $P$ divides $G_1 G_2$ in the ratio $4: 3$ internally
So, $\mathrm{P}=(5 / 7,2 / 7,1 / 7)$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.