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Prove that if a plane has the intercepts...

Prove that if a plane has the intercepts a, b, c and is at a distance of p units from the origin, then `1/a^2 + 1/b^2 + 1/c^2 = 1/p^2`

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The correct Answer is:
`vec(r)*(20hat(i)+23hat(j)-26hat(k))=69`
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Prove that if a plane has intercepts a,b,c and is at a distance of p units from the origin, then 1/a^2+1/b^2+1/c^2=1/p^2 .

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The differential equation of all straight lines which are at a constant distance p from the origin, is (a) (y+xy_1)^(2)=p^(2) (1+y_(1)^2) (b) (y-xy_(1)^(2))=p^(2) (1+y_(1))^(2) ( c ) (y-xy_(1))^(2)=p^(2) (1+y_(1)^(2)) (d) None of these

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BETTER CHOICE PUBLICATION-THREE DIMENSIONAL GEOMETRY -PREVIOUS YEARS BOARD.S QUESTION FOR PRACTICE
  1. Show that the lines (x+3)/-3=(y-1)/1=(z-5)/5 and (x+1)/-1=(y-2)/2=(z-5...

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  2. Prove that the lines : (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-2)/(3)=(y-...

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  3. Prove that if a plane has the intercepts a, b, c and is at a distance ...

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  4. Find the vector equation of the plane through the intersection of the ...

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  5. Find the equation of the plane through the intersection of the planes ...

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  6. Find the equation of the straight line through the point (1,-3,2) and ...

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  7. Find the equation of the straight line passing through the point (2,3,...

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  8. Find the shortest distance between the line vec(r)=hat(i)-7hat(j)-2hat...

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  9. Find the equation of the plane through the point (1,1,1), parallel to ...

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  10. Find the distance between the point with position vector -hat(i)-5hat(...

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  11. Show that the two lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-4)/5=(y-1)/2=z ...

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  12. Show that the lines (x+3)/-3=(y-1)/1=(z-5)/5 and (x+1)/-1=(y-2)/2=(z-5...

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  13. Find the foot of perpendicular drawn from origin to the plane 2x+3y+4z...

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  14. Find the vector equation of the line passing through (1, 2, 3) and per...

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  15. Find the equation of the plane passing through (a, b, c) and parallel ...

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  16. Find the shortest distance between the lines whose vector equations ar...

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  17. Find the shortest distance between the lines whose vector equations ar...

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  18. Find the shortest distance between the lines whose vector equations ar...

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  19. Find the equation of the plane through the points (0,-1,0),(2,1,-1) an...

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  20. Find the equation of the plane passing through the points (0,-1,0),(1,...

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