1
JEE Main 2023 (Online) 24th January Evening Shift
+4
-1 If the foot of the perpendicular drawn from (1, 9, 7) to the line passing through the point (3, 2, 1) and parallel to the planes $$x+2y+z=0$$ and $$3y-z=3$$ is ($$\alpha,\beta,\gamma$$), then $$\alpha+\beta+\gamma$$ is equal to :

A
3
B
1
C
$$-$$1
D
5
2
JEE Main 2023 (Online) 24th January Evening Shift
+4
-1 Let the plane containing the line of intersection of the planes

P1 : $$x+(\lambda+4)y+z=1$$ and

P2 : $$2x+y+z=2$$

pass through the points (0, 1, 0) and (1, 0, 1). Then the distance of

the point (2$$\lambda,\lambda,-\lambda$$) from the plane P2 is :

A
$$2\sqrt6$$
B
$$3\sqrt6$$
C
$$4\sqrt6$$
D
$$5\sqrt6$$
3
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1 The distance of the point (7, $$-$$3, $$-$$4) from the plane passing through the points (2, $$-$$3, 1), ($$-$$1, 1, $$-$$2) and (3, $$-$$4, 2) is :

A
$$4\sqrt2$$
B
4
C
5
D
$$5\sqrt2$$
4
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1 The distance of the point ($$-1,9,-16$$) from the plane

$$2x+3y-z=5$$ measured parallel to the line

$${{x + 4} \over 3} = {{2 - y} \over 4} = {{z - 3} \over {12}}$$ is :

A
13$$\sqrt2$$
B
26
C
20$$\sqrt2$$
D
31
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