Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the distance between the planes $x+2y+3z+7=0$ and $2x+4y+6z+7=0$.

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What is the angle between the planes2x−y+z=6 andx+y+2z=3?

The direction cosines l, m, n of two lines are connected by the relations l + m + n = 0, lm = 0, then the angle between them is:

A line makes angles $α,βandγ$ with the coordinate axes. If $α+β=90_{0},$ then find $γ˙$

Find the vector equation of line passing through the point $(1,2,−4)$ and perpendicular to the two lines: $3x−8 =−16y+19 =7z−10 and3x−15 =8y−29 =−5z−5 $

The line joining the points $(−2,1,−8)and(a,b,c)$ is parallel to the line whose direction ratios are $6,2,and3.$ Find the values of $a,bandc$

The distance of the point (1, -2, 3) from the plane x−y+z=5 measured parallel to the line x2=y3=z−1−6 is

The direction ratios of a normal to the plane through $(1,0,0)and(0,1,0)$ , which makes and angle of $4π $ with the plane $x+y=3,$ are a. $⟨1,2 ,1⟩$ b. $⟨1,1,2 ⟩$ c. $⟨1,1,2⟩$ d. $⟨2 ,1,1⟩$

A mirror and a source of light are situated at the origin 0 and at a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the direction ratios of the normal to the plane are 1, -1, 1, then direction consines of the reflected rays are