Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the equation of the plane passing through the origin and perpendicular to each of the planes $x+2y−z=1$ and $3x−4y+z=5$.

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What is the equation of the plane through z-axis and parallel to the linex−1cosθ=y+2sinθ=z−30?

A line makes the same angle α with each of the x and y axes. If the angleθ, which it makes with the z-axis, is such thatsin2θ=2sin2α, then what is the value ofα?

If θ is the acute angle between the diagonals of a cube, then which one of the following is correct?

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

The equation of the line which passes through the point (1, 1, 1) and intersect the lines x−12=y−23=z−34 and x+21=y−32=z+14 is

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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 a sphere which passes through $(1,0,0)(0,1,0)and(0,0,1),$ and has radius as small as possible.