MCQs of Three Dimensional Geometry

Three Dimensional Geometry MCQs

MCQs of Three Dimensional Geometry

Showing 51 to 60 out of 188 Questions

51.

If the line \frac{x - 3}{2} = \frac{y + 2}{- 1} = \frac{z + 4}{3} lies in the plane lx + my - z = 9, then l^{2} + m^{2} equal to

(a)	5
(b)	2
(c)	26
(d)	18

52.

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

(a)	$\frac{10}{\sqrt{3}}$
(b)	$\frac{20}{3}$
(c)	$\frac{3}{\sqrt{10}}$
(d)	$10 \sqrt{3}$

53.

The shortest distance between the lines

\frac{x}{2} = \frac{y}{2} = \frac{z}{1} and \frac{x + 2}{- 1} = \frac{y - 4}{8} = \frac{z - 5}{4}

lies in the interval :

(a)	(3,4]
(b)	(2,3]
(c)	[1,2)
(d)	[0,1)

54.

The distance of the point (1,-2,4) from the plane passing through the point (1,2,2) and perpendicular to the planes x - y + 2z = 3 and 2x - 2y + z + 12 = 0 is

(a)	2
(b)	$\sqrt{2}$
(c)	$2 \sqrt{2}$
(d)	$\frac{1}{\sqrt{2}}$

55.

If the direction of the lines

\frac{x - 1}{c} = \frac{y + 2}{- 2} = \frac{z - 3}{4}

and

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

are same,c = _____

(a)	-2
(b)	2
(c)	0
(d)	4

56.

The length of perpendicular from the point P(4,-5,3) to the line

\bar{r}

= (5, -2, 6) + k (3, -4, 5),

k \in R

is _____.

(a)	$\frac{\sqrt{457}}{5}$
(b)	$\frac{\sqrt{457}}{5 \sqrt{2}}$
(c)	$\frac{\sqrt{457}}{25}$
(d)	None of the above

57.

The equation of the line parallel to the line

\frac{x - 1}{3} = \frac{2 - y}{- 5} = \frac{z - 10}{15}

and passing through (2, 3, 4) is _____.

(a)	$\bar{r} = (2 + 3 k, 3 + 5 k, 4 + 15 k), k \in R$
(b)	$\bar{r} = (2 - 3 k, 3 - 5 k, 4 - 15 k), k \in R$
(c)	$\bar{r} = (2 + 3 k, 3 - 5 k, 4 + 15 k), k \in R$
(d)	None of the above

58.

The X-intercept formed by the plane 2x - 3y + 6z = 12 is _____.

(a)	6
(b)	12
(c)	4
(d)	-4

59.

The measure of the angle between x + 2y + z = 1 and

\bar{r} = (0, 0, 0) + k (2, 1, - 1), k \in R

is ____.

(a)	$\frac{π}{6}$
(b)	$\frac{π}{3}$
(c)	$\frac{π}{2}$
(d)	$\frac{π}{4}$

60.

The measure of the angle betweeen the plane ax + by + d = 0 and z = 0 (a² + b² ≠ 0) is _____.

(a)	$\frac{π}{3}$
(b)	$c o s^{- 1} \frac{d}{\sqrt{a^{2} + b^{2}}}$
(c)	$\frac{π}{4}$
(d)	$\frac{π}{2}$

Showing 51 to 60 out of 188 Questions