JEE MATHEMATICS MCQ: 3D GEOMETRY SYSTEM

1 Medium

1 of 1

Application +4 | -1

A plane passing through

(1,1,1)

intersects the positive direction at

A, B

and

C

, then the volume of the tetrahedron

O A B C

satisfies (V=Volume)

View answer and explanation

Correct option: B

V \geq \frac{9}{2}

Option B (V ≥ 9/2) is correct because using the equation of a plane and applying AM-GM inequality, the volume of the tetrahedron is greater than or equal to 9/2.

More Questions from 3D GEOMETRY SYSTEM

Practice All Chapter MCQs →

The mid point of the line joining the points

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

and

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

divides the line joining the points

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

and

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

in the ratio The equation of the plane perpendicular to the

y z

-plane and passing through the points

(1,-2,4)

and

(3,-4

5)

is The value of

p

for which the lines

2 x+y-3=0

3 x-y-2=0

and

x-p y+5=0

may intersect at a point is If the vertices of a triangle at

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

and

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

Then, the distance between its circumcentre and orthocentre is The coordinates of the foot of the perpendicular drawn from the point

A(1,0,3)

to the join of the points

B(4,7,1)

and

C(3,5,3)

are The area of the triangle formed by the three lines

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

and

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