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A vector vec( r ) has length 21 and dire...

A vector `vec( r )` has length 21 and directi9on ratio `2,-3,6`. Find the direction cosines and components of `vec( r )` given that `vec( r )` makes an acute angle with X- axis.

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The correct Answer is:
Direction cosine:`2/7,-3/7,6/7`
Componants : `6hati-9hatj+18hatk`
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KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK
  1. A vector vec( r ) has length 21 and directi9on ratio 2,-3,6. Find the ...

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  2. If a vector vecr is in the direction of X- axis then find its directio...

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  3. If a line makes angles alpha,beta and gamma with the positive directio...

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  4. If a line has direction cosines 2/3,-1/3,-2/3, then find its direction...

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  5. Find the direction cosines of the line joining the two points P(-2, 4,...

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  6. Prove that the points P(1,2,3),(3,1,7) and (7,-1,15) are collinear.

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  7. Find the vector equation of the line through the point whose position ...

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  8. The cartesian equation of a line are 6x - 2 = 3y + 1 = 2z - 2. Find it...

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  9. Find the direction cosines of the line (x-2)/(2)=(2y-5)/(-3),z=-1. Als...

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

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

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

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

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

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

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

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

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

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

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

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