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Show that the lines vec r=( hat i+ hat ...

Show that the lines ` vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d vec r=(4 hat i- hat k)+mu(2 hat i+3 hat k)` are coplanar. Also, find the plane containing these two lines.

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Show that the lines vec r=(2 hat j-3 hat k)+lambda( hat i+2 hat j+3 hat k) and vec r=(2 hat i+6 hatj+3 hat k)+mu(2 hat i+3 hat j +4hat k) are coplanar. Also, find the equation of the plane containing them.

Show that the vectors vec a=-2 hat i-2 hat j+4 hat k ,\ vec b=-2 hat i+4 hat j-2 hat k\ a n d\ vec c=4 hat i-2 hat j-2 hat k are coplanar.

Show that the lines vec r=3 hat i+2 hat j-4 hat k+lambda( hat i+2 hat j+2 hat k); vec r=5 hat i-\ 2 hat j+mu(3 hat i+2 hat j+6 hat k) ; are intersecting. Hence find their point of intersection.

Determine the shortest distance between the pair of lines : vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d\ vec r=(2 hat i- hat k)+mu(2 hat i+2 hat k)dot

Find the angle between the lines vec r=(2 hat i-5 hat j+ hat k)+lambda(3 hat i+2 hat j+6 hat k)a n d\ vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k)dot

Find the angle between the lines vec r=3 hat i+2 hat j-4 hat k+lambda( hat i+2 hat j+2 hat k) a n d vec r=(5 hat j-2 hat k)+mu(3 hat i+2 hat j+6 hat k)dot

Statement 1: Lines vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j)a n d vec r=4 hat i- hat k+mu(2 hat i++3 hat k) intersect. Statement 2: vec bxx vec d=0 , then lines vec r= vec a+lambda vec ba n d vec r= vec c+lambda vec d do not intersect.

The distance between the line vec r=(2 hat i-2 hat j+3 hat k)+lambda( hat i- hat j+4 hat k) and plane vec rdot( hat i+5 hat j+ hat k)=5.

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 lines vec r= dot( hat i+2 hat j- hat k)+lambda( hat i- hat j+ hat k) and the plane vec r.(2 hat i- hat j+ hat k)=4.

RD SHARMA ENGLISH-THE PLANE -All Questions
  1. Show that the plane whose vector equation is vec rdot( hat i+2 hat j-...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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