AIEEE 2005 | 3D Geometry Question 313 | Mathematics

The distance between the line

$$\overrightarrow r = 2\widehat i - 2\widehat j + 3\widehat k + \lambda \left( {i - j + 4k} \right),$$ and the plane

$$\overrightarrow r .\left( {\widehat i + 5\widehat j + \widehat k} \right) = 5$$ is

$${{10} \over 9}$$

$${{10} \over {3\sqrt 3 }}$$

$${{3} \over 10}$$

$${{10} \over 3}$$

AIEEE 2005

MCQ (Single Correct Answer)

-1

The angle between the lines $$2x=3y=-z$$ and $$6x=-y=-4z$$ is :

$${0^ \circ }$$

$${90^ \circ }$$

$${45^ \circ }$$

$${30^ \circ }$$

AIEEE 2005

MCQ (Single Correct Answer)

-1

Out of Syllabus

The plane $$x+2y-z=4$$ cuts the sphere $${x^2} + {y^2} + {z^2} - x + z - 2 = 0$$ in a circle of radius

$$3$$

$$1$$

$$2$$

$${\sqrt 2 }$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

A line makes the same angle $$\theta $$, with each of the $$x$$ and $$z$$ axis.

If the angle $$\beta \,$$, which it makes with y-axis, is such that $$\,{\sin ^2}\beta = 3{\sin ^2}\theta ,$$ then $${\cos ^2}\theta $$ equals :

$${2 \over 5}$$

$${1 \over 5}$$

$${3 \over 5}$$

$${2 \over 3}$$

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