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The Cartesian equation of a line is (...

The Cartesian equation of a line is `(x-3)/2=(y+1)/(-2)=(z-3)/5` . Find the vector equation of the line.

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To convert the given Cartesian equation of the line into its vector form, we will follow these steps: ### Step 1: Identify the components of the Cartesian equation The given Cartesian equation is: \[ \frac{x - 3}{2} = \frac{y + 1}{-2} = \frac{z - 3}{5} \] From this equation, we can identify the components: ...
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CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
  1. Find the points where line (x-1)/2=(y+2)/(-1)=z/1 intersects x y ,y za...

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  2. A mirror and source of light are situated at the origin O and a point ...

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  3. The Cartesian equation of a line is (x-3)/2=(y+1)/(-2)=(z-3)/5 . Fi...

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  4. The Cartesian equations of a line are 6x-2=3y+1=2z-2. Find its dire...

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  5. A line passes through the point with position vector 2 hat i-3 hat ...

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  6. Find the plane of the intersection of x^2+y^2+z^2+2x+2y+2=0 and 4x^2...

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  7. Let l1a n dl2 be the two skew lines. If P ,Q are two distinct points o...

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

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  9. Find the angle between the lines 2x=3y=-z and 6x=-y=-4z

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  10. Find the length of the perpendicular drawn from the point(5,4,-1) t...

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  11. The equations of motion of a rocket are x=2t ,y=-4ta n dz=4t , wher...

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  12. Find the shortest distance between the lines vec r=(1-lambda) hat i...

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

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  14. If the lines (x-1)/2=(y+1)/3=(z-1)/4 and (x-3)/1=(y-k)/2=z/1 intersect...

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  15. Find the shortest distance between the z-axis and the line, x+y+2z-3=0...

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  16. The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c a...

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  17. Distance of the point P( vec p) from the line vec r= vec a+lambda ve...

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  18. The direction ratios of a normal to the plane through (1,0,0)a n d(...

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  19. The centre of the circle given by vec rdot( hat i+2 hat j+2 hat k)=...

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  20. Two systems of rectangular axes have the same origin. If a plane cu...

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