AIEEE 2004 | 3D Geometry Question 352 | Mathematics

A line with direction cosines proportional to $$2,1,2$$ meets each of the lines $$x=y+a=z$$ and $$x+a=2y=2z$$ . The co-ordinates of each of the points of intersection are given by :

$$\left( {2a,3a,3a} \right),\left( {2a,a,a} \right)$$

$$\left( {3a,2a,3a} \right),\left( {a,a,a} \right)$$

$$\left( {3a,2a,3a} \right),\left( {a,a,2a} \right)$$

$$\left( {3a,3a,3a} \right),\left( {a,a,a} \right)$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

Out of Syllabus

Distance between two parallel planes

$$\,2x + y + 2z = 8$$ and $$4x + 2y + 4z + 5 = 0$$ is :

$${9 \over 2}$$

$${5 \over 2}$$

$${7 \over 2}$$

$${3 \over 2}$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

Out of Syllabus

The intersection of the spheres
$${x^2} + {y^2} + {z^2} + 7x - 2y - z = 13$$ and
$${x^2} + {y^2} + {z^2} - 3x + 3y + 4z = 8$$
is the same as the intersection of one of the sphere and the plane

$$2x-y-z=1$$

$$x-2y-z=1$$

$$x-y-2z=1$$

$$x-y-z=1$$

AIEEE 2003

MCQ (Single Correct Answer)

-1

Out of Syllabus

The shortest distance from the plane $$12x+4y+3z=327$$ to the sphere

$${x^2} + {y^2} + {z^2} + 4x - 2y - 6z = 155$$ is

$$39$$

$$26$$

$$11{4 \over {13}}$$