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Find the normal unit vector to the plane...

Find the normal unit vector to the plane x+2y+3z-6=0.

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State true or flase for the following statements : A unit normal vector to the plane x + 2y + 3 z - 6 = 0 is (1)/(sqrt(14)) hat(i) + (2)/(sqrt(14)) hat(j) + (3)/(sqrt(14)) hat(k) .

The unit vector normal to the plane x+2y+3z-6=0 is (1)/(sqrt14)hati+(2)/(sqrt14)hatj+(3)/(sqrt14)hatk

Find the equation of the plane containing the line of intersection of the plane x+y+z-6=0\ a n d\ 2x+3y+4z=5=0 and passing through the point (1, 1,1).

Find a unit vector normal to the plane : vecr*(2hati-3hatj+6hatk)+14=0 .

Find the d.r. of the normal to the plane 4x + 3y - z + 6 = 0 and

Find the vector quation of the plane containing the line of intersection of the planes x-3y+4z-5=0 and 2x-y+3z-1=0 and passing through the point (1,-2,3).

Find the equation of the plane, which is perpendicular to the plane 5x + 3y + 6z + 8 = 0 , and which contains the line of intersection of the planes : x + 2y + 3z - 4 = 0 and 2x + y -:- z + 5 = 0 .

Find equation of angle bisector of plane x+2y+3z-z=0 and 2x-3y+z+4=0 .

Direction cosines of the normal to the plane: 2x-3y+4z-6=0 are :

Find the equation of the plane which is perpendicular to the plane 5 x + 3y + 6 z +8 = 0 and which contains the line of intersection of the planes x + 2 y + 3z-4-0 and 2x+y-z+5 -0.

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Show that the lines (x-1)/23=(y+1)/2=(z-1)/5 and (x-2)/4=(y-1)/3=(z+1)...

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  2. Write the vector equation of the following lines and hence find distan...

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  3. Find the normal unit vector to the plane x+2y+3z-6=0.

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  4. Find the unit vector perpendicular to the plane vecr.(6hati+3hatj-2hat...

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  5. Find the cartesian equation of the following planes: vecr.(hati+hatj+h...

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  6. Find the cartesian equation of the following planes: vecr.(2hati-3hatj...

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  7. Find the equations of the line passing through the point (1,-1,2) and...

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  8. Find the equation of the line passing through the point with position ...

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  9. Find the general solution of the following (1+logx)xdy=ydx

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  10. Find the equation of the plane passing through the point (3,-3, 1) and...

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  11. Find the equation of a plane which bisects perpendicularly the line se...

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  12. Find the equation of the plane through the point (1,4,-2) and parallel...

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  13. If the line drawn from (4,-1,2) to the point (-3,2,3) meets a plane at...

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  14. Find the equation of the plane through (1,5,-2) and parallel to the pl...

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  15. The position vectors of two points A and B are 3 hati+hatj+2hatk and h...

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  16. Find the vector equations of the line passing through the point (1,-1,...

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  17. Find the vector equation of the line through the origin, which is perp...

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  18. The vector equation of a plane is vecr.(2hati+2hatj-hatk)=21, find the...

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  19. Find the vector equation of a plane which is at a distance of 5 units ...

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  20. Find the vector equation of a line passing through the point with posi...

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