﻿ IIT - JEE Main Important Questions of Three Dimensional Geometry | Zigya

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# Three Dimensional Geometry

#### Multiple Choice Questions

1.

The distance of the point (1, −5, 9) from the plane x−y+z=5 measured along the line x=y=z is:

• 3√10

• 10√3

• 10/√3

• 20/3

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2.

If the line  lies in the plane lx +my -z = 9, then l2 +m2 is equal to

• 26

• 18

• 5

• 2

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3.

Locus the image of the point (2,3) in the line (2x - 3y +4) + k (x-2y+3) = 0, k ε R is a

• straight line parallel to X - axis

• a straight line parallel to Y- axis

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4.

The distance of the point (1,0,2) from the point of intersection of the line  and the plane x-y +z = 16 is

• 8

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5.

The equation of the plane containing the line 2x-5y +z = 3, x +y+4z = 5 and parallel to the plane x +3y +6z =1 is

• 2x + 6y + 12z = 13

• x+3y+6z = -7

• x+3y +6z = 7

• x+3y +6z = 7

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6.

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

• 3/2

• 5/2

• 7/2

• 7/2

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7.

If the lines

are coplanar, then k can have

• any value

• exactly one value

• exactly two values

• exactly two values

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8.

If the angle between the line x = and the plane x + 2y + 3z = 4 is cos-1  then λ equal

• 2/3

• 3/2

• 2/5

• 2/5

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9.

Statement-1 : The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line:
Statement-2: The line:  bisects the line segment joining A(1, 0, 7) and B(1, 6, 3).

• Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

• Statement-1 is true, Statement-2 is false.

• Statement-1 is true, Statement-2 is false.

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10.

A line AB in three-dimensional space makes angles 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ

• 30°

• 45°

• 60°

• 60°

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