1
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
If x = a, y = b, z = c is a solution of the system of linear equations

x + 8y + 7z = 0

9x + 2y + 3z = 0

x + y + z = 0

such that the point (a, b, c) lies on the plane x + 2y + z = 6, then 2a + b + c equals :
A
$$-$$ 1
B
0
C
1
D
2
2
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
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
$${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = 9$$
3
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
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
4
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
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)
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