MCQs of Three Dimensional Geometry

Three Dimensional Geometry MCQs

MCQs of Three Dimensional Geometry

Showing 41 to 50 out of 188 Questions

41.

Statement -1 : The point A(3,1,6) is the mirror image of the point B(1,3,4) in the plane x - y + z = 5 Statement -2 : The plane x - y + z = 5 bisects the line segment joining A(3,1,6) and B(1,3,4)

(a)	Statement -1 is true; Statement -2 is true; Statement -2 is not a correct explanation of Statement -1.
(b)	Statement -1 is true; Statement -2 is false
(c)	Statement -1 is false; Statement -2 is true
(d)	Statement -1 is true; Statement -2 is true; Statement -2 is a correct explanation of Statement -1.

42.

A equation of a plane parallel to the plane x - 2y + 2z - 5 = 0 and at a unit distance from the origin is :

(a)	x - 2y + 2z - 3 = 0
(b)	x - 2y + 2z + 1 = 0
(c)	x - 2y + 2z - 1 = 0
(d)	x - 2y + 2z + 5 = 0

43.

Let Q be the foot of the perpendicular from the origin to the plane 4x - 3y + z +13 = 0 and R be a point R(-1,1,-6) on the plane. Then length QR = _____

(a)	$\sqrt{14}$
(b)	$\sqrt{\frac{19}{2}}$
(c)	$3 \sqrt{\frac{7}{2}}$
(d)	$\frac{3}{\sqrt{2}}$

44.

The image of the line

\frac{x - 1}{3} = \frac{y - 3}{1} = \frac{z - 4}{- 5}

in the plane 2x - y + z + 3 = 0 is the line :

(a)	$\frac{x + 3}{3} = \frac{y - 5}{1} = \frac{z - 2}{5}$
(b)	$\frac{x + 3}{- 3} = \frac{y - 5}{- 1} = \frac{z + 2}{5}$
(c)	$\frac{x - 3}{3} = \frac{y + 5}{1} = \frac{z - 2}{- 5}$
(d)	$\frac{x - 3}{- 3} = \frac{y + 5}{- 1} = \frac{z - 2}{5}$

45.

Equation of the plane which passes through the point of intersection of lines

\frac{x - 1}{3} = \frac{y - 2}{1} = \frac{z - 3}{2} and \frac{x - 3}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}

and has the largest distance from the origin is :

(a)	7x + 2y +4z = 54
(b)	3x + 4y + 5z = 49
(c)	4x + 3y + 5z = 50
(d)	5x + 4y + 3z = 57

46.

A symmetrical form of the line of intersection of the planes x = ay + b and z = cy + d is

(a)	$\frac{x - b}{a} = \frac{y - 1}{1} = \frac{z - d}{c}$
(b)	$\frac{x - b - a}{a} = \frac{y - 1}{1} = \frac{z - d - c}{c}$
(c)	$\frac{x - b}{b} = \frac{y - 0}{1} = \frac{z - c}{d}$
(d)	$\frac{x - b - a}{b} = \frac{y - 1}{0} = \frac{z - d - c}{d}$

47.

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 :

(a)	2x + 6y +12z = 13
(b)	x + 3y + 6z = -7
(c)	x + 3y + 6z = 7
(d)	2x + 6y + 12z = -13

48.

If the points (1,1,λ) and (-3, 0,1) are the equidistant from the plane, 3x + 4y - 12z + 13 = 0, then λ satisfies the equation :

(a)	3x² - 10x + 7 = 0
(b)	3x² + 10x + 7 = 0
(c)	3x² + 10x - 13 = 0
(d)	3x² - 10x + 21 = 0

49.

If the shortest distance between the lines

\frac{x - 1}{α} = \frac{y + 1}{- 1} = \frac{z}{1}, (α \neq - 1)

and x + y + z + 1 = 0 = 2x - y + z + 3 is

\frac{1}{\sqrt{3}}

then a value of α is :

(a)	$- \frac{16}{19}$
(b)	$- \frac{19}{16}$
(c)	$\frac{32}{19}$
(d)	$\frac{19}{32}$

50.

The shortest distance between the Z - axis and the line x + y + 2z - 3 = 0 = 2x + 3y + 4z - 4, is :

(a)	1
(b)	2
(c)	3
(d)	4

Showing 41 to 50 out of 188 Questions