MCQs of Three Dimensional Geometry

Showing 181 to 188 out of 188 Questions

181.

The equation of the plane passing through (3,2,0) and the line

\frac{x - 3}{1} = \frac{y - 6}{5} = \frac{z - 4}{4}

is _____

182.

The equation of the plane passing through the line of intersection of the planes x + y + z = 1 and 2x+3y-z+4=0 and paarallel to X-axis is _____

183.

If M is the midpoint of the line segment joining

A (4 \hat{i} + 5 \hat{j} + 10 \hat{k})

and

B (- \hat{i} + 2 \hat{j} + \hat{k})

then the perpendicular of the plane passing through M and perpendicular to

\bar{AB}

is _____

(a)	$\bar{r} \cdot (- 5 \hat{i} - 3 \hat{j} + 11 \hat{k}) + \frac{135}{2} = 0$
(b)	$\bar{r} \cdot (\frac{3}{2} \hat{i} + \frac{7}{2} \hat{j} - \frac{9}{2} \hat{k}) + \frac{235}{2} = 0$
(c)	$\bar{r} \cdot (4 \hat{i} + 5 \hat{j} + 10 \hat{k}) + 4 = 0$
(d)	$\bar{r} \cdot (- \hat{i} + 2 \hat{j} + \hat{k}) + 4 = 0$

184.

The image of the point (-1,3,4) in the plane x-2y=0 is _____

185.

The point P (3,2,6) is in space and Q is on the line

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

for

μ =_____\vec{PQ}

is parallel to the plane x-4y+3z=1.

186.

A plane passes through (1,-2,1) and it is perpendicular to the planes 2x-2y+z=0 and x-y+2z=4, then the distance of the plane from (1,2,2) is _____

187.

The equation of the plane containing the line and perpendicular to the lines

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

as well as

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

is _____

188.

If the distance between the plane containing the lines

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

and

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

and the plane Ax-2y+z=d is

\sqrt{6}

then

|6|

Showing 181 to 188 out of 188 Questions