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Find the vector and cartesian equations of the plane which passes through the point (5, 2, - 4) and perpendicular to the line with direction ratios 2, 3, -1.

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The correct Answer is:
vector equations `[vecr - (5hati + 2hatj - 4hatk)] · (2hati + 3hatj - hatk) = 0,` cartesian equations 2x + 3y -z= 20)
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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-TEXTBOOK IILUSTRATIONS FOR PARCTICE WORK
  1. Find the shortest distance between the lines l1 and l2 whose vector eq...

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  2. Find the distance between the lines l1 and l2 given by vecr=hati+2hatj...

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  3. Find the vector equation of the plane which is at a distance of (6)/(s...

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  4. Find the direction cosines of the unit vector perpendicular to the pla...

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  5. Find the distance of the plane 2x – 3y + 4z - 6 = 0 from the origin.

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  6. Find the coordinates of the foot of the perpendicular drawn from the o...

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  7. Find the vector and cartesian equations of the plane which passes thro...

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  8. Find the vector equations of the plane passing through the points R(2,...

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  9. Find the equation of the plane with intercepts 2, 3 and 4 on the x, y ...

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  10. Find the vector equation of the plane passing through the intersection...

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  11. Show that the lines (x+3)/(-3)=(y-1)/(1)=(z-5)/(5) and (x+1)/(-1)=(y-2...

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

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  13. Find the angle between the two planes 3x – 6y + 2z = 7 and 2x + 2y – 2...

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  14. Find the distance of a point (2, 5, -3) from the plane vecr.(6hati-3ha...

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  15. Find the angle between the line (x+1)/(2)=y/3=(z-3)/(6) and the plane ...

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  16. A line makes the angle alpha, beta , gamma and delta with the diagonal...

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  17. Find the equation of the plane that contains the point (1,-1, 2) and i...

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  18. Find the distance between the point P (6,5, 9) and the plane determine...

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

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  20. Find the coordinates of the point where the line through the points A ...

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