JEE MATHEMATICS MCQ: 3D GEOMETRY SYSTEM

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Analyzing +4 | -1

Four lines drawn from the vertices of any tetrahedron to the centroid of the opposite faces meet in a point whose distance from each vertex is

k

times the distance from each vertex to the opposite face, where

k

View answer and explanation

Correct option: C

\frac{3}{4}

Option C (

\frac{3}{4}

) is correct because the centroid of a tetrahedron divides the line joining a vertex to the centroid of the opposite face in the ratio 3:1.

More Questions from 3D GEOMETRY SYSTEM

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\left( { - 10,\;8} \right)

\left( { - 6,\;12} \right)

\left( {4,\; - 2} \right)

\left( { - 2,\;4} \right)

y z

(1,-2,4)

(3,-4

5)

p

2 x+y-3=0

3 x-y-2=0

x-p y+5=0

O\left( {0,0} \right),A\left( {a,0} \right)

B\left( {0,a} \right).

A(1,0,3)

B(4,7,1)

C(3,5,3)

\frac{x}{1}=\frac{y}{2}=\frac{z}{3}, \frac{x}{2}=\frac{y}{1}=\frac{z}{3}

\frac{x-1}{1}=\frac{2-y}{2}, z=3