Geometry

3D Coordinate Geometry

3D Coordinate Geometry - Problem Solving

         

Determine the value of b b such that the line x14=y2b=z9 \frac{x-1}{4} = \frac{y-2}{b} = \frac{z}{9} does not intersect the plane 2x4y+5z=6. 2x- 4y + 5z = 6.

If the angle between the line x=y42=z1λ x= \frac{y-4}{2}=\frac{z-1}{\lambda} and the plane x+3y+z=1 x + 3y + z = 1 is cos1(1011), \cos ^{ -1 }{ \left( \sqrt { \frac { 10 }{ 11 } } \right) }, what is λ? \lambda?

Find the symmetric point of A=(4,4,16) A = (4, 4, 16) to the plane π:x+y+z=21. \pi : x+ y+z=21.

Let α,β,\alpha,\beta, and γ\gamma be the angles that the line x23=y+14=z+35\frac{x-2}{3}=-\frac{y+1}{4}=\frac{z+3}{5} forms with the xyxy-, yzyz-, and xzxz-planes. Then what is the value of sin2α+sin2β+sin2γ?\sin^2\alpha+\sin^2\beta+\sin^2\gamma?

What is the volume of the region bounded by the plane 7x+8y+9z504=07x+8y+9z-504=0 and the xyxy-, yzyz-, and xzxz-planes?

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