Class 12

Math

3D Geometry

Three Dimensional Geometry

If a line makes angles $α,β$ and $γ$ with the x-axis, y-axis and z-axis respectively then $(sin_{2}α+sin_{2}β+sin_{2}γ )=$

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If $A(3,2,−4),B(5,4,−6)andC(9,8,−10)$ are three collinear points, then find the ratio in which point $C$ divides $AB˙$

Find the equations of the bisectors of the angles between the planes $2x−y+2z+3=0and3x−2y+6z+8=0$ and specify the plane which bisects the acute angle and the plane which bisects the obtuse angle.

If Q is the image of the point P(2, 3, 4) under the reflection in the plane x−2y+5z=6, then the equation of the line PQis

Find the equation of the plane passing through the straight line $2x−1 =−3y+2 =5z $ and perpendicular to the plane $x−y+z+2=0.$

The shortest distance from the plane To the sphere is

The vector a⃗ =αi^+2j^+βk^ lies in the plane of the vectors b⃗ =i^+j^ and c⃗ =j^+k^ and bisects the angle between b⃗ andc⃗ . Then which one of the following gives possible values of a and b?

Find the equation of the plane which is parallel to the lines $r=i^+j^ +λ(2i^+j^ +4k^)and−3x+1 =2y−3 =1z+2 $ and is passing through the point $(0,1,−1$ ).

Show that the lines $α−δx−a+d =αy−a =α+δz−a−d $ and $β−γx−b+c =βy−b =β+γz−b−c $ are coplanar.