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Prove that the lines (x+1)/3=(y+3)/5=(z+...

Prove that the lines `(x+1)/3=(y+3)/5=(z+5)/7a n d(x-2)/1=(y-4)/4=(z-6)/7` are coplanar . Also, find the plane containing these two lines.

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To prove that the lines \(\frac{x+1}{3} = \frac{y+3}{5} = \frac{z+5}{7}\) and \(\frac{x-2}{1} = \frac{y-4}{4} = \frac{z-6}{7}\) are coplanar, we can follow these steps: ### Step 1: Identify the direction ratios and points of the lines The first line can be expressed in parametric form: - Direction ratios: \( (3, 5, 7) \) - Point on the line: \( (-1, -3, -5) \) The second line can be expressed in parametric form: ...
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Prove that the lines (x+1)/(3)=(y+3)/(5)=(z+5)/(7) and (x-2)/(1)=(y-4)/(4)=(z-6)/(7) are coplanar. Also, find the plane containing these two lines

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RD SHARMA-THE PLANE -Solved Examples And Exercises
  1. Find the equation of the plane through the intersection of the planes ...

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  2. Show that the plane whose vector equation is vec rdot( hat i+2 hat j-...

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  3. Prove that the lines (x+1)/3=(y+3)/5=(z+5)/7a n d(x-2)/1=(y-4)/4=(z-6)...

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  4. Show that the lines vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat ...

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  5. Find the distance of the point P(-1,-5,-10) from the point of intersec...

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  6. Find the distance of the point (1,-2,3) from the plane x-y+z=5 measure...

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  7. Show that the plane whose vector equation is vec r*( hat i+2 hat j= h...

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  8. Find the equation of the plane passing through the point (0,7,-7) and...

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  9. Find the equation of the plane passing through the points (1,-1,2)a n ...

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  10. Find the equation of the plane passing through the point whose coor...

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  11. Find the equation of the plane passing through the point (1,1,-1)a n d...

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  12. Find the equation of the plane passing through the point (-1,-1,2)a n ...

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  13. Find the angle between the planes x+y+2z=9a d n2x-y+z=15.

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  14. If the planes Find the angle between the planes vec rdot(2 hat i- hat...

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  15. Find the vector equation of the plane passing through the points 3 hat...

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  16. Find the angle between the planes vec rdot(2 hat i- hat j+ hat k)=6a ...

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

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  18. Find the vector equation of the plane passing through the points A(a ,...

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  19. Reduce the equation vec rdot(3 hat i-4 hat j+12 hat k)=5 to normal fo...

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  20. Find the vector equation of a plane which is at a distance of 8 units ...

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