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Find the vector and the Cartesian equations of the line through the point (5, 2, - 4) and which is parallel to the vector `3hati+2hatj-8hatk.`
`vecr=(5+3lambda)hati+(2+2lambda)hatj+(-4-8lambda)hatk` and certesian equations `(x-5)/(3)=(y-2)/(2)=(z+4)/(-8)`

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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-TEXTBOOK IILUSTRATIONS FOR PARCTICE WORK
  1. Find the direction cosines of x, y and z- axis.

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  2. Show that the points A(2, 3, -4), B(1, - 2, 3) and C(3, 8, - 11) are c...

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  3. Find the vector and the Cartesian equations of the line through the po...

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  4. Find the vector equation for the line passing through the points (-1, ...

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  5. The Cartesian equation of a line is (x+3)/(2)=(y-5)/(4)=(z+6)/(2) ...

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  6. Find the angle between the lines vecr = (3 + lambda)hati + 2(1 + l...

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  7. The angle "bet"^(n) two line ( x+3)/(3) = (y-1)/(5) = (z +3)/(4...

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  8. Find the shortest distance between the lines l1 and l2 whose vector eq...

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

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

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

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

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

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

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

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

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

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

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

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

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