1
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
Out of Syllabus
If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of $$\Delta$$ABC is :
A
$${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = 1$$
B
$${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = 3$$
C
$${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = {1 \over 9}$$
D
$${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = 9$$
2
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
Out of Syllabus
If the line, $${{x - 3} \over 1} = {{y + 2} \over { - 1}} = {{z + \lambda } \over { - 2}}$$ lies in the plane, 2x−4y+3z=2, then the shortest distance between this line and the line, $${{x - 1} \over {12}} = {y \over 9} = {z \over 4}$$ is :
A
2
B
1
C
0
D
3
3
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
Out of Syllabus
The coordinates of the foot of the perpendicular from the point (1, $$-$$2, 1) on the plane containing the lines, $${{x + 1} \over 6} = {{y - 1} \over 7} = {{z - 3} \over 8}$$ and $${{x - 1} \over 3} = {{y - 2} \over 5} = {{z - 3} \over 7},$$ is :
A
(2, $$-$$4, 2)
B
($$-$$ 1, 2, $$-$$1)
C
(0, 0, 0)
D
(1, 1, 1)
4
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
Out of Syllabus
The line of intersection of the planes $$\overrightarrow r .\left( {3\widehat i - \widehat j + \widehat k} \right) = 1\,\,$$ and
$$\overrightarrow r .\left( {\widehat i + 4\widehat j - 2\widehat k} \right) = 2,$$ is :
A
$${{x - {4 \over 7}} \over { - 2}} = {y \over 7} = {{z - {5 \over 7}} \over {13}}$$
B
$${{x - {4 \over 7}} \over 2} = {y \over { - 7}} = {{z + {5 \over 7}} \over {13}}$$
C
$${{x - {6 \over {13}}} \over 2} = {{y - {5 \over {13}}} \over { - 7}} = {z \over { - 13}}$$
D
$${{x - {6 \over {13}}} \over 2} = {{y - {5 \over {13}}} \over 7} = {z \over { - 13}}$$
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