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Consider the Cartesian equation of a lin...

Consider the Cartesian equation of a line `(x-3)/2=(y+1)/3=(z-5)/(-2)`
i.Find its vector equation.
ii. Find its intersecting point with the plane 5x+2y-6z-7=0

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The cartesian equation of a line is (x+3)/2=(y-5)/4 =(z+6)/2 . Find its vector equation .

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If the cartesian equation of the plane 2x-y+2z=3 find the vector equation of the plane in standard form.

Find the equation of the projection of the line (x-1)/2=(y+1)/(-1)=(z-3)/4 on the plane x+2y+z=9.

Find the image of the point (1, 2, 3) in the line (x-6)/(3)=(y-7)/(2)=(z-7)/(-2) .

Find the vector and cartesian equations of the plane containing the line (x-2)/(2)=(y-2)/(3)=(z-1)/(-2) and passing through the point (-1, 1,-1).

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NEW JOYTHI PUBLICATION-THREE DIMENSIONAL GEOMETRY-Objective
  1. Consider the Cartesian equation of a line (x-3)/2=(y+1)/3=(z-5)/(-2) ...

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  2. The distance between x axis and the point (3,12,5) is

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  3. The perpendicular distance of the point (6,5,8) from y-axis

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  4. If 1/2,1/3,n are the direction cosines of a line , then the value of ...

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  5. A line makes angles of 45^@ and 60^@ with the z-axis and the x-axis re...

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  6. If direction cosines of a line are (1)/(c),(1)/(c),(1)/(c)," then. "

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  7. The coordinates of a point P are (3,12,4) w.r.t. the origin O. Then th...

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  8. The direction cosines of a line that makes equal angles with the three...

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  9. If the direction cosines of a line are k,k,k , then

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  10. The direction cosines of a straight line, whose projections on the coo...

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  11. The vector equation of the straight line (1-x)/3 =(y+1)/(-2) =(3-z)/(-...

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  12. The line (x-x1)/0=(y-y1)/1=(z-z1)/2 is

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  13. A unit vector parallel to the straight line (x-2)/3=(3+y)/(-1) = (z-2)...

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  14. The two lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d will be perpendicul...

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  15. If the vector equation of a line (x-2)/2=(2y-5)/(-3) =z+1 is vecr=2hat...

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

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  17. The equation of the line joining the points (-3,4,11) and (1,-2,7) is

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  18. The vector equation of the line 6x-3=3y+4=2z-2 is

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  19. The angle between the staight lines (x+1)/2=(y-2)/5=(z+3)/4 and (x-1)/...

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  20. If the lines (x-1)/(-3)=(y-2)/(2k) =(z-3)/2 and (x-1)/(3k) =(y-5)/1=(z...

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  21. A line makes angles alpha,beta,gamma with the coordinates axes . If al...

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