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Find the vector equation of the plane ...

Find the vector equation of the plane passing through the points `(2,\ 1,\ -1)\ a n d\ (-1,\ 3,\ 4)` and perpendicular to the plane `x\ -\ 2y+4z=10` . Also show that the plane thus obtained contains the line ` vec r=- hat i+3 hat j+4 hat k+lambda\ (3 hat i-2 hat j-\ 5 hat k)dot`

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Find the vector equation of the plane passing through the points (3, 4, 2) and (7, 0, 6) and perpendicular to the plane 2x-5y-15=0. Also, show that the plane thus obtained contains the line vec r= hat i+3 hat j-2 hat k+lambda( hat i- hat j+ hat k)dot

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane -> r(dot( hat i+2 hat j-5 hat k))=9.

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane vec r.( hat i+2 hat j-5 hat k)+9=0 .

Find the vector equation of a plane passing through a point having position vector 2 hat i- hat j+ hat k and perpendicular to the vector 4 hat i+2 hat j-3 hat kdot

Find the vector equation of a line passing through 3 hat i-5 hat j+7 hat k and perpendicular to the plane 3x-4y+5z=8.

Find the vector equation of the plane passing through the points 3 hat i+4 hat j+2 hat k ,2 hat i-2 hat j- hat ka n d7 hat i+6 hat kdot

Find the vector equation of the line passing through the point (1,2,3) and parallel to the planes vec rdot( hat i- hat j+2 hat k)=5 and vec rdot(3 hat i+ hat j+ hat k)=6.

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Find the equation of the line passing through the point hat i+ hat j- hat k and perpendicular to the lines vec r= hat i+lambda(2 hat i+ hat j-3 hat k)a n d vec r=(2 hat i+ hat j- hat k)dot

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RD SHARMA ENGLISH-THE PLANE -All Questions
  1. Find the vector equation of the plane passing through the points (1, ...

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  2. Show that the planes 2x+6y-6z=7\ a n d\ 3x+4y+5z=8 are at right angles...

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  3. Find the vector equation of the plane passing through the points (2,...

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  4. Find the angle between the plane: vec rdot((2 hat i-3 hat j+4 hat k)=...

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  5. Find the angle between the plane: vec rdot((2 hat i- hat j+2 hat k)=6...

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  6. Find the angle between the plane: vec rdot((2 hat i+3 hat j-6 hat k)=...

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  7. Find the angle between the plane: 2x-y+z=4\ a n d\ x+y+2z=3

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  8. Find the angle between the plane: x-y+z=5\ a n d\ x+2y+z=9

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  9. Find the angle between the two planes 2x + y-2z = 5and 3x- 6y-2z = 7...

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  10. Find the angle between the plane: x+y-2z=3\ a n d\ 2x-2y+z=5 .

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  11. Find the angle between the plane: 2x-3y+4z=1\ a n d-x+y=4.

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  12. Show that the following planes are at right angle: vec rdot((2 hat i-...

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  13. Show that the following planes are at right angle: x-2y+4z=10\ a n d\ ...

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  14. Determine the value of lambda for which the following plane are perpen...

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  15. Determine the value of lambda for which the following plane are perpen...

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  16. Determine the value of lambda for which the following plane are perpen...

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  17. Obtain the equation of the plane passing through the point (1, -3, -2)...

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  18. Find the equation of the plane through the points (2,2,1) and (9,3,6) ...

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  19. Find the equation of the plane with intercept 3 on the y-axis and para...

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  20. Find dy/dx if x + 2y = 8.

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