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Show that the points hat i- hat j+3 hat...

Show that the points ` hat i- hat j+3 hat ka n d3( hat i+ hat j+ hat k)` are equidistant from the plane ` vec rdot(5 hat i+2 hat j+ hat k)+9=0` and lie on opposite sides of it.

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The points hat(i)-hat(j)+3hat(k) and 3hat(i)+3hat(j)+3hat(k) are equidistant from the plane rcdot(5hat(i)+2hat(j)-7hat(k))+9=0 , then they are

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Find the angle between the line vec r = (2 hat i-hat j +3 hat k)+ lambda (3 hat i-hat j+2 hat k ) and the plane vec r.(hat i + hat j + hat k)=3

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i- hat k) are collinear.

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Find the equation of the plane through the point 2 hat i+ hat j- hat k and passing through the line of intersection of the plane vec rdot(( hat i+3 hat j- hat k)=0\ a n d\ vec rdot(( hat j+2 hat k)=0.

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RD SHARMA ENGLISH-THE PLANE -All Questions
  1. Find the distance of the point 2 hat i+ hat j- hat k from the plane v...

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  2. Find the distance of the point (21,0) from the plane 2x+y+2z+5=0.

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  3. Show that the points hat i- hat j+3 hat ka n d3( hat i+ hat j+ hat k)...

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  4. Find the equations of the planes parallel to the plane x-2y+2z-3=0 whi...

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

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  6. Find the equation of the plane passing through the intersection of ...

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  7. Find the equation of the plane passing through the intersection of the...

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

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  9. Two systems of rectangular axes have the same origin. If a plane cuts ...

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  10. A variable plane is at a constant distance p from the origin and meets...

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  11. Find the equation of the plane passing through the intersection of the...

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  12. Find the equation of the plane through the line of intersection of ve...

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  13. Find the equation of the plane which is perpendicular to the plane 5x+...

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  14. Find the equation of a plane through the intersection of the planes v...

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  15. Find the vector equation of the following plane in non-parametric fo...

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  16. Find the vector equation of the plane vec r=(1+s-t) hat i+(2-s) hat ...

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  17. Find the Cartesian form the equation of the plane vec r=(s-2t) hat i...

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  18. Find the vector equation of the following plane in scalar product form...

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

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

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