MCQs of Three Dimensional Geometry

Three Dimensional Geometry MCQs

MCQs of Three Dimensional Geometry

Showing 161 to 170 out of 188 Questions

161.

Find the distance between the plane

\bar{r} \cdot (2 \hat{i} - \hat{j} + 3 \hat{k}) = 4

and

\bar{r} \cdot (6 \hat{i} - 3 \hat{j} + 9 \hat{k}) + 13 = 0 .

(a)	$\frac{5}{3 \sqrt{14}}$
(b)	$\frac{10}{3 \sqrt{14}}$
(c)	$\frac{25}{3 \sqrt{14}}$
(d)	None of the above

162.

Obtain the direction of the line intersection of the planes 2x+y+z=1 and 3x+2y-z=3

(a)	(3,5,1)
(b)	(3,5,-1)
(c)	(-3,5,1)
(d)	none of the above

163.

The measure of the angles between the line 2x=3y=-z and

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

is _____

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

164.

Find the co-ordinates of foot of perpendicular from point P(1,-2,3) to the line

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

(a)	$(- \frac{1}{7}, - \frac{5}{7}, \frac{11}{7})$
(b)	$(\frac{1}{7}, - \frac{5}{7}, \frac{11}{7})$
(c)	$(\frac{1}{7}, \frac{5}{7}, \frac{11}{7})$
(d)	$(- \frac{1}{7}, \frac{5}{7}, \frac{11}{7})$

165.

The equation of the plane passing through the intersection of the planes x + 2y +3z + 4 = 0 and 4x + 3y + 2z + 1 = 0 and passing through origin is _____ .

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

166.

If the line

\frac{x + 1}{3 k} = \frac{y + 3}{2} = \frac{z - 4}{5}

and plane 2x-3y-4z=12 are parallel, then find k

(a)	$- \frac{3}{13}$
(b)	$\frac{3}{13}$
(c)	$- \frac{13}{3}$
(d)	$\frac{13}{3}$

167.

the measure of the angle between the lines

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

and

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

is _____

(a)	$\cos^{- 1} \frac{1}{65}$
(b)	$\frac{π}{6}$
(c)	$\frac{π}{3}$
(d)	$\frac{π}{4}$

168.

The shortest distance between the lines

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

and

\frac{x - 2}{3} = \frac{y - 4}{4} = \frac{z - 5}{5}

is _____

(a)	$\frac{1}{6}$
(b)	$\frac{1}{\sqrt{6}}$
(c)	$\frac{1}{\sqrt{3}}$
(d)	$\frac{1}{3}$

169.

The equation of the plane passing through A(2, -1, 3) and parallel to the vectors

\bar{a} = (3, 0, - 1)

and

\bar{b} = (- 3, 2, 2)

is _____

(a)	2x - 3y + 6z - 25 = 0
(b)	2x - 3y + 6z + 25 = 0
(c)	3x - 2y + 6z - 25 = 0
(d)	3x - 2y + 6z + 25 = 0

170.

The shortest distance between the line

\frac{x - 3}{3} = \frac{y - 8}{- 1} = \frac{z - 3}{1}

and

\frac{x + 3}{- 3} = \frac{y + 7}{2} = \frac{z - 6}{4}

(a)	$\sqrt{30}$
(b)	$2 \sqrt{30}$
(c)	$5 \sqrt{30}$
(d)	$3 \sqrt{30}$

Showing 161 to 170 out of 188 Questions