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

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Find the equation of the plane which contain the line of intersection of the plane vecr.(hati+2hatj+3hatk)-4=0 and vecr.(2hati+hatj-hatk)+5=0 and which is perpendicular to the plane 5x+3y-6z+8=0 .

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

Find the equations of the plane which contains the line of intersections of the planes vecr.(hati-2hatj+3hatk)-4=0 and vecr.(-2hati+hatj+hatk)+5=0 and whose intercept on x-axis is equal to the on y-axis.

Find the vector equation of the plane passing through the intersection of the planes vecr cdot (hati+hatj+hatk) = 6 and vecr cdot(2hati + 3hatj+4hatk) = -5 , and the point (1, 1, 1).

Find the vector equation of the plane passing through the intersection of the planes vecr cdot (2hati+2hatj-3hatk) = 7, vecr cdot(2hati + 5hatj + 3hatk) = 9 and through the point (2, 1, 3)

Find the equation of the plane passing through (a, b, c) and parallel to the plane vecr cdot(hati + hatj + hatk) = 2

Find the equation of the plane passing through the line of intersection of the planes : vecr*(hati+3hatj)-6=0 and vecr*(3hati-hatj-4hatk)=0 , whose perpendicular distance form origin is unity.

Find the vector equation of the plane passing through the intersection of the planes vecr.(hati+hatj+hatk) =6 and vecr.(2hati+3hatj+4hatk)=-5 and point (1,1,1)

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane vecr cdot(hati+2hatj-5hatk) + 9 = 0

Find the vector equation of the plane passing through the intersection of the planes : vecr*(2hati-hatj+2hatk)=2 and vecr*(3hati+hatj-2hatk)=-2 and perpendicular to the veca=5hati-2hatj+3hatk .

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE
  1. Find the equation of the plane passing through the line of intersectio...

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  2. If O be the origin and the coordinates of P be (1, 2, – 3), then find ...

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

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  4. Find the distance of the point (-1 , -5 , -10) from the point of inter...

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

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

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  7. Prove that if a plane has intercepts a,b,c and is at a distance of p u...

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  8. Find the Distance between the two planes 2x+3y+4z=4 and 4x+6y+8z=12

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  9. The planes 2x - y + 4z = 5 and 5x - 2.5y + 10z = 6 are :

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  10. The x, co-ordinate of a point on the line joining the points Q (2, 2, ...

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  11. Find the distance of the point (-1 , -5 , -10) from the point of inter...

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  12. Find the equation of a plane which is at a distance 3sqrt3 units from ...

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  13. Find the equation of the two lines through the origin which intersect ...

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  14. The plane ax+by=0 is rotated through an angle alpha about its line of ...

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  15. Show that the sequence t n defined by t n = 3 n + 1 is an AP.

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  16. Prove that the lines, whose direction cosines are given by al+bm+cn=0,...

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  17. Prove that the lines, whose direction cosines are given by al+bm+cn=0,...

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  18. Using converse of Basic Proportionality theorem prove that the line jo...

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  19. Verify that <(l1+l2+l3)/sqrt3,(m1+m2+m3)/sqrt3,(n1+n2+n3)/sqrt3> can b...

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

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