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Show that the plane whose vector equatio...

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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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.

Show that the line whose vector equation is vec r=(2 hat i-2 hat j+3)+lambda( hat i- hat j+4 hat k) is parallel to the plane whose vector equation vec r( hat i+5 hat j+ hat k)=5 . Also, find the distance between them.

Show that the line whose vector equation is vec rdot(2 hat i+5 hat j-7 hat k)+lambda( hat i+3 hat j+4 hat k) is parallel to the plane whose vector equation is vec rdot( hat i+ hat j- hat k)=7 . Also find the distance between them.

Find the shortest distance between the lines whose vector equations are: vec r=2 hat i- hat j- hat k+lambda(2 hat i-5 hat j+2 hat k)a n d\ , vec r= hat i+2 hat j+ hat k+ mu( hat i- hat j+ hat k)dot

Find the shortest distance between the lines whose vector equations are vec r= hat i+ hat j+lambda(2 hat i- hat j+ hat k) and vec r=2 hat i+ hat j- hat k+mu(3 hat i-5 hat j+2 hat k)dot

Find the shortest distance between the following pairs of line whose vector equation are: vec r=( hat i+2 hat j+3 hat k+lambda(2 hat i+3 hat j+4 hat k)a n d\ vec r=(2 hat i+4 hat j+5 hat k)+mu(3 hat i+4 hat j+5 hat k)

Find the shortest distance between the following pairs of line whose vector equation are: vec r=(3 hat i+5 hat j+7 hat k)+lambda( hat i-2 hat j+7 hat k)a n d\ vec r=- hat i- hat j- hat k+mu(7 hat i-2 hat j+ hat k)

Find the shortest distance between the following pairs of line whose vector equation are: vec r=3 hat i+8 hat j+3 hat k+lambda(3 hat i- hat j+ hat k)a n d\ vec r=-3 hat i-7 hat j+6 hat k+mu(-3 hat i+2 hat j+4 hat k)

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 magnitude of vector vec a=(3 hat k+4 hat j)xx( hat i+ hat j- hat k)dot

RD SHARMA ENGLISH-THE PLANE -All Questions
  1. Find the distance of the point P(-1,-5,-10) from the point of intersec...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Find the vector equation of a plane which is at a distance of 8 units ...

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  17. Find the direction cosines of perpendicular from the origin to the ...

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  18. Find the coordinates of the foot of the perpendicular drawn from the ...

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  19. Find the equation of a plane which is at a distance of 3sqrt(3) units ...

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  20. Find the equation of the plane passing through the point (-1,2,1) and ...

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