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Show that the plane whose vector equatio...

Show that the plane whose vector equation is ` vec rdot( hat i+2 hat j- hat k)=1.` and the line whose vector equation is ` vec r=(- hat i+ hat j+ hat k)+lambda(2 hat i+ hat j+4 hat k)` are parallel. Also, find the distance between them.

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Show that the plane whose vector equation is vec r*( hat i+2 hat j= hat k)=3 contains the line whose vector equation is vec r*( hat i+ hat j)+lambda(2 hat i+ hat j+4 hat k)dot

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Find the angle between the planes whose vector equations are vec r.(2 hat i+2 hat j-3 hat k)=5 and vec r.(3 hat i-3 hat j+5 hat k)=3 .

Find the Cartesian form of equation of a plane whose vector equation is : vec rdot((- hat i+ hat j+2 hat k)=9

Find the shortest distance between the lines vec r=( hat i+2 hat j+ hat k)+lambda( hat i- hat j+ hat k) and vec r=(2 hat i- hat j- hat k)+mu(2 hat i+ hat j+2 hat k)

Find the angle between the vectors vec a= hat i+hat j-hat k and vec b=hat i-hat j+hat k

Write the cartesian equation of the following line given in vector form : vec r=2 hat i+ hat j-4 hat k+lambda\ ( hat i- hat j- hat k)

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RD SHARMA ENGLISH-THE PLANE -All Questions
  1. Find the distance between the point with position vector hat i-5 hat ...

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

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  3. Show that the plane whose vector equation is vec rdot( hat i+2 hat j-...

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  4. Prove that the lines (x+1)/3=(y+3)/5=(z+5)/7a n d(x-2)/1=(y-4)/4=(z-6)...

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  5. Show that the lines vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat ...

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  6. Find the distance of the point P(-1,-5,-10) from the point of intersec...

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  7. Find the distance of the point (1,-2,3) from the plane x-y+z=5 measure...

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  8. Show that the plane whose vector equation is vec r*( hat i+2 hat j= h...

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  9. Find the equation of the plane passing through the point (0,7,-7) and...

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  10. Find the equation of the plane passing through the points (1,-1,2)a n ...

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  11. Find the equation of the plane passing through the point whose coor...

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  12. Find the equation of the plane passing through the point (1,1,-1)a n d...

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  13. Find the equation of the plane passing through the point (-1,-1,2)a n ...

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  14. Find the angle between the planes x+y+2z=9a d n2x-y+z=15.

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  15. If the angle between the planes vec rdot.(2 hat i- hat j+lambda hat k...

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  16. Find the vector equation of the plane passing through the points 3 hat...

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  17. Find the angle between the planes vec rdot(2 hat i- hat j+ hat k)=6a ...

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  18. Find the vector equation of the plane passing through the points (1,1,...

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  19. Find the vector equation of the plane passing through the points A(a ,...

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  20. Reduce the equation vec r (dot(3 hat i-4 hat j+12 hat k ))=5 to norma...

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