MCQs of Three Dimensional Geometry

Three Dimensional Geometry MCQs

MCQs of Three Dimensional Geometry

Showing 171 to 180 out of 188 Questions

171.

If the direction ratios of two lines are given by 3lm-4ln+mn=0 and l+2m+3n=0, then the measure of the angle between them is _____

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

172.

The line passing through the origin and containing the line

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

is _____

(a)	x + 5y -3z = 0
(b)	x - 5y + 3z = 0
(c)	x - 5y - 3z = 0
(d)	3x - 10y + 5z = 0

173.

A line makes angles of equal measures θ with X-axis and Z-axis. If it makes an angle of measure β with Y-axis and sin²β=3 sin²θ then cos²θ =_____

(a)	$\frac{3}{5}$
(b)	$\frac{1}{5}$
(c)	$\frac{2}{3}$
(d)	$\frac{2}{5}$

174.

For what values of k,

(\frac{1}{\sqrt{2}}, \frac{1}{2}, k)

becomes direction cosines of a line ?

(a)	$\pm \frac{1}{2}$
(b)	$Only \frac{1}{2}$
(c)	$Only - \frac{1}{2}$
(d)	For any real number

175.

The equation of th plane passing through (2, 3, 1) and (4, -5, 3) and parallel to X-axis is _____

(a)	x + 4z = 7
(b)	y - 4z = 7
(c)	y + 4z = -7
(d)	y + 4z = 7

176.

Which of the following points lie on the line

\bar{r} = (- 5 \hat{i} + 2 \hat{j} + 3 \hat{k}) + μ (9 \hat{i} + 5 \hat{j} + 3 \hat{k})

μ \in R

(a)	(-41,22,-8)
(b)	(-14,-7,0)
(c)	(13,-8,8)
(d)	(-50,27,-12)

177.

The equation of the plane passing through the line of intersection of the planes x+2y+3z=4 and 2x+y-z=-5 and perpendicular to the plane 5x+3y+6x+8=0 is _____

(a)	7x-2y+3z+81=0
(b)	23x+14y-9z+48=0
(c)	51x+15y-50z+173
(d)	None of the above

178.

The equation of the plane

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

and parallel to X-axis is _____

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

179.

If the direction cosines of perpendicular lines are given by al + bm + cn=0 and fmn + gnl +hlm=0, then _____

(a)	$\sqrt{af} + \sqrt{bg} + \sqrt{ch} = 0$
(b)	$\frac{a^{2}}{f} + \frac{b^{2}}{g} + \frac{c^{2}}{h} = 0$
(c)	$\frac{f}{a} + \frac{g}{b} + \frac{h}{c} = 0$
(d)	$a^{2} f + b^{2} g + c^{2} h = 0$

180.

If P (0,1,0) are Q (0,0,1) are two points, then projection of

\vec{PQ}

on the plane x+y+z=3 is _____

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

Showing 171 to 180 out of 188 Questions