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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)`

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The correct Answer is:
`vec(r) = (hat(i) + 2 hat(j) - 4 hat(k)) + lambda (2 hat(i) + 3 hat(j) + 6 hat(k))`
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OSWAAL PUBLICATION-THREE DIMENSIONAL GEOMETRY-Topic -2 (Short answer type questions-II)
  1. Find the shortest distance between the lines L(1) " and " L(2) ...

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  2. Find the coordinates of the foot of perpendicular drawn from th poi...

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  3. Find the distance of the point (-1,-5,-10) from the point of intersect...

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  4. Find the direction cosines of the line (x+2)/2=(2y-7)/6=(5-z)/6dot Als...

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  5. Find the shortest distance between two lines whose vector equations ar...

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  6. Show that the lines (x+1)/(3)=(y+3)/(5) =(z+5)/(7) " and " (x-2)/(1...

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  7. Show that the lines (5-x)/-4=(y-7)/4=(z+3)/-5 and (x-8)/7=(2y-8)/2=(z-...

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  8. Show that the lines vec(r)= vec(i)+vec(j)-vec(k)+lambda(3 vec(i)- vec(...

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  9. The equation of line passing through (3,-1,2) and perpendicular to the...

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  10. Find the equation of the line passing through the point (2, 1, 3) and ...

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  11. Find the values of p so that the lines (1-x)/3=(7y-14)/(2p)=(z-3)/2an...

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  12. Find the shortest distance between the lines whose vector equations ar...

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  13. Find the equation of the perpendicular drawn from the point (2,4,-1) t...

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  14. Using vectors show that the points A(-2,3,5),B(7,0,-1)C(-3,-2,-5) and ...

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  15. Show that the lines vec(r ) =(hat(i) -hat(j)) +lambda (2hat(i)+ ha...

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  16. Find the Vector and Cartesian equations of the line passing through...

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  17. Find the shortest distance between the following pair of lines : (...

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  18. 2/ Find the perpendicular distance of the point (1, 0, 0) from the lin...

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  19. Find the shortest distance between the following lines whose vector...

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  20. Find the angle between the following pair of lines: (-x+2)/(-2)=(y-...

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