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Show that the lines (x-5)/(7) = (y+2)/(-...

Show that the lines `(x-5)/(7) = (y+2)/(-5) = (z)/(1)` and `(x)/(1) = (y)/(2) = (z)/(3)`  are perpendicular to each other.

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Show that the lines (x - 5)/(4) = (y - 7)/(4) = (z + 3)/(-5) and (x - 8)/(7) = (y - 4)/(1) = (z - 5)/(3) intersect each other.

For what value of k lines (x + 2)/(-k) = (y - 3)/(2) = (z + 4)/(k) and (x - 4)/(5) = (y - 3)/(k) = (z + 1)/(2) are perpendicular to each other?

Show that the line (5-x)/(-4) = (y-7)/( 4) = (z+3)/(-5) and (x-8)/( 7) = (2y-8)/( 2) = (z-5)/(3) are coplanar.

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ARIHANT PUBLICATION-THREE-DIMENSIONAL GEOMETRY-Chapter Practice
  1. If a line has direction ratios 2, -1, 2, then determine its direction ...

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  2. If P is a point in space such that OP = 12 and OP is inclined at angle...

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  3. Show that the lines (x-5)/(7) = (y+2)/(-5) = (z)/(1) and (x)/(1) = (y)...

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  4. What is the angle between two planes 3x - 4y + 5z = 0 and 2x - y - 2z ...

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  5. Write the direction cosines of the normal to plane 3x+4y +12z = 52

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  6. Find the cartesian equation of the plane vec(r).[(s-2t) hat(i) + (3-t)...

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  7. What is the cartesian equation of the line vec(r)=(3hat(i) - hat(j) + ...

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  8. Write the vector equation ofthe line given by (x - 5)/3 = (y + 4)/7 = ...

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  9. Cartesian equation of line AB is (2x-1)/(2) = (4-y)/(7) = (z+1)/(2). W...

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  10. Find the equation of line passing through the point (2, 1, 3) having t...

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  11. Find the equation of a line parallel to Y-axis and passing through the...

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  12. Find the coordinates of the point, where the line passing through (5, ...

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  13. Write the condition for the lines vec(r) = vec(a)(1) + lambda vec(b)(1...

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  14. Find the equation of the plane passing through the point(-1,-1, 2) and...

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  15. Find the equation of the plane passing through the intersection of the...

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  16. Find the vector and cartesian equation of the line passing through the...

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  17. Find the vector equation of the plane determined by the points A(3,-1,...

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  18. Find the coordinates of the point where the line through the points A(...

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  19. Find the point of intersection of the line (x-2)/(1) = (y+2)/(3) = (z-...

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  20. Find the vector and cartesian equations of line passing through the po...

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