1
IIT-JEE 2008 Paper 2 Offline
+3
-1
Consider the lines

$${L_1}:{{x + 1} \over 3} = {{y + 2} \over 1} = {{z + 1} \over 2}$$

$${L_2}:{{x - 2} \over 1} = {{y + 2} \over 2} = {{z - 3} \over 3}$$

The unit vector perpendicular to both $${L_1}$$ and $${L_2}$$ is :

A
$${{ - \widehat i + 7\widehat j + 7\widehat k} \over {\sqrt {99} }}$$
B
$${{ - \widehat i - 7\widehat j + 5\widehat k} \over {5\sqrt 3 }}$$
C
$${{ - \widehat i + 7\widehat j + 5\widehat k} \over {5\sqrt 3 }}$$
D
$${{7\widehat i - 7\widehat j - \widehat k} \over {\sqrt {99} }}$$
2
IIT-JEE 2008 Paper 2 Offline
+3
-1

Consider the lines,

$${L_1}:{{x + 1} \over 3} = {{y + 2} \over 1} = {{z + 1} \over 2}$$

$${L_2}:{{x - 2} \over 1} = {{y - 2} \over 2} = {{z - 3} \over 3}$$

The distance of the point $$(1, 1, 1)$$ from the plane passing through the point $$(-1, -2, -1)$$ and whose normal is perpendicular to both the lines $${L_1}$$ and $${L_2}$$ is :
A
$${2 \over {\sqrt {75} }}$$
B
$${7 \over {\sqrt {75} }}$$
C
$${13 \over {\sqrt {75} }}$$
D
$${23 \over {\sqrt {75} }}$$
3
IIT-JEE 2008 Paper 2 Offline
+3
-1

Consider the lines,

$${L_1}:{{x + 1} \over 3} = {{y + 2} \over 1} = {{z + 1} \over 2}$$

$${L_2}:{{x - 2} \over 1} = {{y - 2} \over 2} = {{z - 3} \over 3}$$

The shortest distance between $${L_1}$$ and $${L_2}$$ is :

A
$$0$$
B
$${17 \over {\sqrt 3 }}$$
C
$${41 \over {5\sqrt 3 }}$$
D
$${17 \over {5\sqrt 3 }}$$
4
IIT-JEE 2008 Paper 2 Offline
+3
-1

Consider three points $$P = ( - \sin (\beta - \alpha ), - cos\beta ),Q = (cos(\beta - \alpha ),\sin \beta )$$ and $$R = (\cos (\beta - \alpha + \theta ),\sin (\beta - \theta ))$$ where $$0 < \alpha ,\beta ,\theta < {\pi \over 4}$$. Then :

A
P lies on the line segment RQ
B
Q lies on the line segment PR
C
R lies on the line segment QP
D
P, Q, R are non-collinear
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