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The cartesian equations of a line are 3x...

The cartesian equations of a line are 3x + 1 = 6y - 2 = 1 - z. Find the fixed point through which it passes, its direction ratios and also its vector equation.

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The correct Answer is:
`(-1/3,1/3,1):2,1,-6`
`vecr=-1/3hati+1/3hatj+hatk+lambda(2hati+hatj-6hatk)`
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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK
  1. Find the direction cosines of the line (x-2)/(2)=(2y-5)/(-3),z=-1. Als...

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  2. If the points A(-1, 3, 2), B(-4, 2, -2) and C(5, 5, lambda) are collin...

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  3. The cartesian equations of a line are 3x + 1 = 6y - 2 = 1 - z. Find th...

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  4. Find the vector equation of a line passing| through (2, -1, 1) and par...

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  5. squareABCD is a parallelogram. The position vectors of the points A, B...

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  6. Find the coordinates of the point where the line through (5, 1, 6) and...

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

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  8. Find the angle between the lines whose direction cosines are given by ...

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

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

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

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  12. Find the shortest distance between the lines vecr =(8+3lambda) hati - ...

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  13. Find the shortest distance between the lines vecr=(4hati-hatj)+lam...

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  14. Find the shortest distance between the lines (x-1)/(2)=(y-2)/(3)=(...

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  15. Find the shortest distance between the lines vecr=(lambda-1)hati+(...

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  16. Find the direction cosines of perpendicular from the origin to the pla...

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  17. Find the vector equation of a plane which is at a distance 11 units fr...

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  18. Find the vector equation of the plane vecr=hati-hatj+lambda(hati+hatj+...

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  19. Find the cartesian equation of the plane through the point (2,-1, 1) a...

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  20. Find the vector equation of the plane passing through the points (1, -...

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