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Find the vector and Cartesian forms of the equation of the plane passing through the point `(1,\ 2,\ -4)` and parallel to the lines ` vec r=( hat i+2 hat j-4 hat k)+lambda(2 hat i+3 hat j+6 hat k)a n d\ vec r=( hat i-3 hat j+5 hat k)+mu( hat i+ hat j- hat k)dot` Also find the distance of the point (9, -8, -10) from the plane thus obtained.

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RD SHARMA ENGLISH-THE PLANE -All Questions
  1. Find the equation of the plane passing through the points (2, 2, -1) a...

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  2. Find the coordinates of the point, where the line (x-2)/3=(y+1)/4=(z-2...

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  3. Find the vector and Cartesian forms of the equation of the plane pas...

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  4. Find the equation of the plane passing through the point (3,4,1) an...

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  5. Find the coordinates of the point, where the line (x-2)/3=(y+1)/4=(z-2...

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  6. Find the vector equation of the line passing through (1, 2, 3) and p...

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  7. Find the vector equation of the line passing through (1, 2, 3 ) and ...

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  8. Find the value of lambda such that the lines (x-2)/6=(y-1)/lambda=(z+5...

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  9. Find the equation of the plane passing through the points (-1,2,0),(2,...

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  10. Find the coordinates of the point where the line through the points...

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  11. Find the coordinate of the point where the line through (5, 1, 6) and ...

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  12. Find the coordinates of the point where the line through (3, -4, -5...

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  13. Find the distance of the point P(3,\ 4,\ 4) from the point where the l...

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  14. Show that the lines (x-a+d)/(alpha-delta)=(y-a)/alpha=(z-a-d)/(alph...

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  15. If 4x+4y-lambdaz=0 is the equations of the plane through the origin th...

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

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

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

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