Class 12

Math

3D Geometry

Three Dimensional Geometry

Show that the following pairs of planes are at right angles.$x−2y+4z=10$ and $18x+17y+4z=49$.

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Find the angle between the line $r=i^+2j^ −k^+λ(i^−j^ +k^)$ and the plane $r2i^−j^ +k^˙ =4.$

A line makes angles, θ,ϕ and ψ with x, y, z axes respectively. Consider the following:$1.sin2θ+sin2ϕ=cos2ψ$2. cos2θ+cos2ϕ=sin2ψ$3.sin2θ+cos2ϕ=cos2ψ$Which of the above is/are correct?

If $r=(i^+2j^ +3k^)+λ(i^−j^ +k^)$ and $r=(i^+2j^ +3k^)+μ(i^+j^ −k^)$ are two lines, then the equation of acute angle bisector of two lines is

A line passes through the points $(6,−7,−1)and(2,−3,1)˙$ Find te direction cosines off the line if the line makes an acute angle with the positive direction of the x-axis.

The equation of the plane which makes with co-ordinate axes, a triangle with its centroid (α,β,γ)is

Which one of the following is the plane containing the lien x−22=y−33=z−45 and parallel to z axis?

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

Under which one of the following condition will the two planes x+y+z=7 andαx+βy+γz=3, be parallel (but not coincident)?