Class 12

Math

3D Geometry

Three Dimensional Geometry

Show that the lines $−45−x =4y−7 =−5z+3 $ and $7x−8 =22y−8 =3z−5 $ are coplanar. Find the equation of the plane containing these lines.

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Find the distance between the line $−3x+1 =2y−3 =1z−2 $ and the plane $x+y+z+3=0.$

The number of planes that are equidistant from four non-coplanar points is a. $3$ b. $4$ c. $7$ d. $9$

The intercept made by the plane $rn˙=q$ on the x-axis is a. $i^n˙q $ b. $qi^n˙ $ c. $qi^n˙ $ d. $∣n∣q $

If $P_{1}:r.n_{1}−d_{1}=0$ $P_{2}:r.n_{2}−d_{2}=0$ and $P_{3}:r.n_{3}−d_{3}=0$ are three non-coplanar vectors, then three lines $P_{1}=0$, $P_{2}=0$; $P_{2}=0$,$P_{3}=0$ ; $P_{3}=0$ $P_{1}=0$ are

The ratio in which the line segment joining the points whose position vectors are $2i^−4j^ −7k^and−3i^+5j^ −8k^$ is divided by the plane whose equation is $r^i^−2j^ +3k^˙ =13$ is a. $13:12$ internally b. $12:25$ externally c. $13:25$ internally d. $37:25$ internally

The equation of the plane which passes through the point of intersection of lines $3x−1 =1y−2 =2z−3 ,and1x−3 =2y−1 =3z−2 $ and at greatest distance from point $(0,0,0)$ is a. $4x+3y+5z=25$ b. $4x+3y=5z=50$ c. $3x+4y+5z=49$ d. $x+7y−5z=2$

Find the points where line $2x−1 =−1y+2 =1z $ intersects $xy,yzandzx$ planes.

Find the angle between the lines whose direction cosines are connected by the relations $l+m+n=0and2lm+2nl−mn=0.$