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The plane l x+m y=0 is rotated through a...

The plane `l x+m y=0` is rotated through an angle `alpha` about its line of intersection with the plane z=0 . Prove that the equation of the plane in its new position is `l x+m ypm(sqrt(l^2+m^2)tanalpha)z=0.`

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RD SHARMA ENGLISH-THE PLANE -All Questions
  1. Find the vector equation of the following plane in scalar product form...

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  2. The plane x-2y+3z=0 is rotated through a right angle about the line of...

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  3. The plane l x+m y=0 is rotated through an angle alpha about its line o...

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  4. Find the vector equation of the line passing through the point (1,-1,2...

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  5. Find the vector equation of the plane passing through the intersection...

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  6. If 30 oxen can plough 1/7th of the field in 4 hrs , in how many hour w...

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  7. Find the equation of the plane through the points (1,0,-1),(3,2,2) and...

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  8. Find the angle between line (x+1)/3=(y-1)/2=(z-2)/4 and the plane 2x+y...

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  9. Show that the line whose vector equation is vec r=(2 hat i-2 hat j+3)...

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  10. Show that the line whose vector equation is vec rdot(2 hat i+5 hat j-...

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  11. Find the vector equation of the line passing through the point (1,-1,2...

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  12. Show that the line vec r= hat i+ hat j+lambda(2 hat i+ hat j+4 hat k)...

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  13. Find the plane passing through (4,-1,2) and parallel to the lines (x+2...

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  14. Find the angle between the lines vec r= dot( hat i+2 hat j- hat k)+la...

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  15. Find the angle between the lines x-2y+z=0=x+2y-2za n dx+2y+z=0=3x+9y+5...

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  16. Find the distance between the parallel planes, vec r.(2 hat i-3 hat j...

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  17. Find the distance between the parallel planes 2x-y+2z+3=0a n d4x-2y+4z...

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  18. Find the distance between the parallel planes vec r.( hat i+2 hat j+3...

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  19. Find the equation of the plane which passes through the point (3,4,-1)...

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  20. Find the distance of the point (3, 3, 3) from the plane vec r.(5 hat ...

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