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Find the vector equation of the line passing through the point `(1," "2," "" "4)` and perpendicular to the two lines: `(x-8)/3=(y+19)/(-16)=(z-10)/7` and `(x-15)/3=(y-29)/8=(z-5)/(-5)`

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The correct Answer is:
`vec(r) = (hati + 2hatj -4 hatk ) + lambda (2 hati + 3 hatj + 6 hatk)`
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Find the vector equation of line passing through the point (1,2,-4) and perpendicular to the two lines: (x-8)/(3)=(y+19)/(-16)=(z-10)/(7) and (x-15)/(3)=(y-29)/(8)=(z-5)/(-5)

Find the Vector and Cartesian equations of the line passing through the point (1,2,4) and perpendicular to the two lines (x-8)/(3)=(y+19)/(-16)=(z-10)/(7) and (x-15)/(3)=(y-29)/(8)=(z-5)/(-5)

(i) Find the vector and cartesian equation of the line passing through the point (1,2,-4) and perpendicular to the two lines : (x - 8)/(3) = (y + 19)/(-16) = (z - 10)/(7) and (x - 15)/(3) = (y - 19)/(8) = (z - 5)/(-5) . (ii) Find the vector and cartesian equations of the line passing through the point (2,1,3) and perpendicular to the lines : (x -1)/(1) = (y -2)/(2) = (z - 3)/(3) and (x)/(-3) = (y)/(2) = (z)/(5) .

Find the vector equation of the line passing through the point (1,-1,2) and perpendicular to the plane 2x-y+3z-5=0

Find the vector equation of the line passing through the point (1,-1,2) and perpendicular to the plane 4x-2y-5z-2=0

Find the vector and Cartesian equations of the line passing through the point (1,2-4) and perpendicular to each of the lines (x-8)/(3)=(y+19)/(-16) =(z-10)/(7) " and " (x-15)/(3)=(y+29)/(8) =(z-5)/(-5)

Find the vector equation of line passing through point (1,2,-4) and perpendicular to two lines (x-8)/(3)=(y+19)/(-16)=(z-10)/(7) and (x-15)/(3)=(y-25)/(8)=(z-5)/(-5)

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MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY -REVISION EXERCISE
  1. If the direction cosines of a variable line in two adjacent points be ...

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  2. Prove that the straight lines whose direction cosines are given by the...

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  3. Prove that the line joining the mid-points of the two sides of a tr...

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

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  5. Prove that the lines x=ay +b,z =cy +d and x=a'y +b' z =c'y +a' ...

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  6. Prove that the line joining the points vec(6a) - vec(4b) + vec(4c) and...

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

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  8. Find the vector equation of the line passing through the point (1,"...

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  9. find the coordinates of point where the line through (3,-4,-5) and (2,...

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  10. Show that equation of the plane passing through a point having positio...

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  11. Find the distance of the point (2,3,4) from the plane 3x+2y+2z+5=0 mea...

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  12. Find the distance of the point with position vector - hati - 5 hatj - ...

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  13. Find the point R, Where the line joining P (1,3,4) and Q (-3,5,2) cuts...

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  14. Find the equation of the plane passing through the line of intersectio...

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  15. If from a point P(a ,b ,c) perpendiculars P Aa n dP B are drawn to Y Z...

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  16. If O be the origin and the coordinates of P be(1," "2," "" "3) , th...

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  17. Find the equation of the plane , which contains the line of intersecti...

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  18. Prove that the shortest distance between the diagonals of a rectangula...

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  19. A variable plane is at a constant distance p from the origin and meets...

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