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Find the equation of a plane passing thr...

Find the equation of a plane passing through (1, 1, 1) and parallel to the lines `L_1` and `L_2` direction ratios (1, 0,-1) and (1,-1, 0) respectively. Find the volume of the tetrahedron formed by origin and the points where this plane intersects the coordinate axes.

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CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
  1. If the angle between the plane x-3y+2z=1 and the line (x-1)/2=(y-1)/...

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  2. The length of projection of the line segment joining the points (1,...

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  3. Find the equation of a plane passing through (1, 1, 1) and parallel to...

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  4. Find the equation of the plane passing through the points(2,1,0),(5,0,...

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  5. For the line (x-1)/(1)=(y-2)/(2)=(z-3)/(3), which one of the following...

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  6. The value of m for which straight lein 3x-2y+z+3=0=4 x-3y+4z+1 is pa...

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  7. Let the equations of a line and plane be (x+3)/2=(y-4)/3=(z+5)/2a n...

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  8. The length of the perpendicular form the origin to the plane passin...

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  9. In a three-dimensional x y z space , the equation x^2-5x+6=0 represent...

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  10. The line (x-2)/3=(y+1)/2=(z-1)/-1 intersects the curve x y=c^(2),z=0 i...

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  11. A unit vector parallel to the intersection of the planes vec r. \ (...

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  12. Let L1 be the line vec r1=2 hat i+ hat j- hat k+lambda(hat i+2 hat k)...

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  13. The distance of point A(-2,3,1) from the line P Q through P(-3,5,2), w...

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  14. The Cartesian equation of the plane vec r=(1+lambda-mu) hat i+(2-l...

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  15. Find the angle between the lines vec r=3 hat i+2 hat j-4 hat k+lambda...

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  16. The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambd...

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  17. Let L be the line of intersection of the planes 2x""+""3y""+""z""=""...

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  18. Statement 1: there exists a unique sphere which passes through the ...

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  19. Statement 1: There exist two points on the (x-1)/1=y/(-1)=(z+2)/2 w...

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  20. Statement 1: The shortest distance between the lines x/(-3)=(y-1)/1=(z...

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