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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)=3` contains the line whose vector equation is ` vec rdot( 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 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

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 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 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 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 Cartesian form of equation of a plane whose vector equation is : vec rdot((12 hat i-3 hat j+4 hat k)+5=0

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

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 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

RD SHARMA ENGLISH-THE PLANE -All Questions
  1. 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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  2. The line through of the plane passing through the lines (x-4)/(1)=(y-3...

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Find the co-ordinates of the foot of perpendicular and the length of p...

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  19. Find the distance of the point with position vector -hat i-5 hat j-10...

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  20. Find the length and the foot of the perpendicular from the point (1, 1...

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