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Find the equation of the plane which con...

Find the equation of the plane which contains the line of intersection of the planes `vecr.(hati+2hatj+3hatk)-4=0,vecr.(2 hati +hatj-hatk)+5=0` and which is perpendicular to the planer `vecr.(5 hat i -6 hatk)+8=0`

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Find the equation of plane passing through the intersection of the planes vecr*(hati+hatj+hatk)=1 and vecr*(2hati+3hatj-hatk)+4=0 and parallel x-axis.

Find the equation of the plane through the intersection of the planes vecr.(hat(i) + 3hat(j)) - 6 = 0 and vecr.(3hat(i) - hat(j) - 4hat(k)) = 0 , whose perpendicular distance from origin is unity.

Find the vector equation of the plane passing through the intersection of the planes vecr.(hat(i) + hat(j) + hat(k)) = 6 and vecr.(2hat(i) + 3hat(j) + 4hat(k))= - 5 and the point (1, 1, 1).

Find the direction consines of the perpendicular from the origin to the plane r(6 hati - 3 hatj - 2 hatk) + 3=0

Vectors vecP=hati+2hatj+3hatk and vecQ=2hati+ahatj-5hatk are perpendicular .Find a.

If veca = 3hati+hatj-2hatk, vecb = 2hati-3hatj+4hatk then verify that vecaxxvecb is perpendicular to both veca and vecb .

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SHARAM PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXAMPLE
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  2. Passing throughthe point (2,-3,1) and (-1,1-7) and perpendicular to th...

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  3. Write the axis to which the plane by+cz+d=0 is parallal.

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  4. Find the shortest distance between the lines (x-1)/(2) = (y-2)/(3) =...

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  5. Find the equation of the plane which contains the line of intersection...

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  6. Prove that the lines (x + 3)/(2) = (y + 5)/(3) = (z - 7)/(-3) and (x +...

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  7. Prove that the four points (0, 4, 3), (-1, -5, -3), (-2, -2, 1) and (1...

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  8. Find the distance from the line x/2 = y/3 = z/1 to the point (4, 5, 2)...

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  9. A variable plane is at a constant distance 3r from the origin and meet...

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  10. If the edges of a rectangular parallelopiped are of lengths a, b, c, t...

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  11. If l1,m1,n1andl2,m2,n2 are the direction cosines of two mutually perpe...

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  12. Find the image of the point (2, 3, 4) with respect to the plane x - y ...

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  13. Prove that the two lines whose direction cosines are connected by the ...

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  14. Find the equation of the plane through the points (2, 2,1)and (9, 3, 6...

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  15. How far is the point (4, 1, 1) from the line of intersection of the pl...

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  16. passing through the point (-1,3,2) perpendicular to the planes x+2y+...

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  17. Find the point of intersection of the line (x-2)/3 = (y + 1)/4 = (z - ...

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  18. Prove that the line joining (1,2,3),(2,1,-1) intersects the line joini...

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  19. Find the equation of the line through the point (1, -2, 1) and paralle...

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  20. Find the shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/...

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