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Show that the lines vec r=(2 hat j-3 ha...

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.

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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)

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

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

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.

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

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RD SHARMA ENGLISH-THE PLANE -All Questions
  1. If 4x+4y-lambdaz=0 is the equations of the plane through the origin th...

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  2. If the lines (x-1)/2=(y+1)/3=(z-1)/4a n d(x-3)/1=(y-k)/2=z/1 intersect...

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

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

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  5. The line through of the plane passing through the lines (x-4)/(1)=(y-3...

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

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  7. Find the vector equation of the plane passing through the points (3, ...

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  8. If the lines (x-1)/(-3)=(y-2)/(-2k)=(z-3)/2 and (x-1)/k=(y-2)/1=(z-3)...

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  9. Find the vector equation of the plane passing through three points w...

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  10. Show that the lines (x-5)/4=(y-7)/4=(z+3)/(-5) and (x-8)/7=(y-4)/1=(z-...

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  11. Find the equation of a plane which passes through the point (3, 2, ...

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  12. Find the shortest distance between the lines (x-2)/(-1)=(y-5)/2=(z-0)/...

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  13. Find the shortest distance between the lines , (x-1)/2=(y-3)/4=(z+2)/1...

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  14. Find the length and the foot of the perpendicular from the point (7...

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  15. Find the image of the point O(0,0,0) in the plane 3x+4y-6z+1=0

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  16. Find the reflection of the point (1,\ 2,\ -1) in the plane 3x-5y+4z=5.

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

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

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

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  20. Find a vector in the direction of vec a=2 hat i- hat j+2 hat k , whic...

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