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If the lines (x-1)/-3 = (y-2)/(2k) = (z-...

If the lines `(x-1)/-3 = (y-2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 = (z-6)/-5`
are perpendicular, then find the value of k.

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The correct Answer is:
The direction ratios of the two lines are -3, 2k, 2 and 3k, 1, -5 respectively
Since the lines are perpendicular, `-3xx3k+2kxx1+2xx-5=0`
`rArr` -9k+2k-10=0
`rArr` 7k=-10 `rArr = (-10)/7`
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A N EXCEL PUBLICATION-THREE DIMENSTIONAL GEOMETRY-QUESTION BANK
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  2. If the co-ordinates of the points A, B, C, D be (1,2,3),(4,5,7) (-4,3,...

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  3. If the lines (x-1)/-3 = (y-2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 ...

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

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  5. Find the eqation of the plane passing through (a,b,c) and parallel to ...

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  6. Find the shortest distance between the lines vecr = 6hati+2hatj+2hatk+...

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  7. Find the co-ordinates of the point where the line through (5,1,6) and ...

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  8. Find the co-ordinates of the point where the line through (5,1,6) and ...

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  9. Find the co-ordinates of the point where the line through (3, -4, -5) ...

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

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  11. If the points (1,1,p) and (-3,0,1) be equidistant from the plane vecr....

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

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  13. If O be the origin and the co-ordinates of P be (1,2,-3), then find th...

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  14. Find the equation of the plane which contains the line of intersectio...

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  15. Find the distance of the point (-1,-5,-10) from the point of intersecț...

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

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  17. Find the vector equation of the line passing through the point (1,2,-4...

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  18. Prove that if a plane has the intercepts a, b, c and it is at a distan...

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  19. Distance between the two planes: '2 x+3 y+4 z=4' and '4 x+6 y+8 z=(12)...

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  20. Choose the correct answer. The planes 2x-y+4z=5 and 5x-2.5y+10z=6 are...

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