Class 12

Math

3D Geometry

Three Dimensional Geometry

Write the angle between the line $2x−1 =1y−2 =−2z+3 $ and the plane $x+y+4=0$.

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Find the equation of the image of the plane $x−2y+2z−3=0$ in plane $x+y+z−1=0.$

If the straight lines $x=−1+s,y=3−λs,z=1+λsandx=2t ,y=1+t,z=2−t,$ with paramerters $sandt,$ respectivley, are coplanar, then find $λ˙$

Find the angel between the lines $2x=3y=−zand6x=−y=−4z˙$

Find the equation of the plane passing through the points $(1,0,−1)and(3,2,2)$ and parallel to the line $x−1=21−y =3z−2 ˙$

What is the distance between the planesx−2y+z−1=0 and−3x+6y−3z+2=0?

Find the equation of the sphere which passes through $(10,0),(0,1,0)and(0,0,1)$ and whose centre lies on the plane $3x−y+z=2.$

Find the point where line which passes through point $(1,2,3)$ and is parallel to line $r=i^+j^ +2k^+λ(i^−2j^ +3k^)$ meets the xy-plane.

Consider the following relations among the anglesα, β and γ made by a vector with the coordinate axes$I.cos2α+cos2β+cos2γ=−1$II. sin2α+sin2β+sin2γ=1$Whichoftheaboveias recorrect?$