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The Cartesian equations of a line are...

The Cartesian equations of a line are `6x-2=3y+1=2z-2.` Find its direction ratios and also find a vector equation of the line.

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To solve the problem, we need to find the direction ratios of the line given by the Cartesian equations \(6x - 2 = 3y + 1 = 2z - 2\) and then derive the vector equation of the line. ### Step-by-Step Solution: 1. **Write the given equations**: The given equation is: \[ 6x - 2 = 3y + 1 = 2z - 2 ...
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CENGAGE ENGLISH-THREE DIMENSIONAL GEOMETRY-All Questions
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  3. The Cartesian equations of a line are 6x-2=3y+1=2z-2. Find its dire...

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

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

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

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

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

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

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

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

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