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Show that the line 3x - 2y + 5 = 0 , y +...

Show that the line 3x - 2y + 5 = 0 , y + 3z - 15 = 0 and `(x -1)/(5) = (y + 5)/(-3) = (z)/(1)` are perpendicular to each other .

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

(i) Show that the line (x+3)/(2) = (y+1)/(-1) = (z+3)/(3) and (x)/(5) = (y-5)/(1) = (z-3)/(-3) are perpendicular. (ii) Show that the lines (x-4)/(-2) = (y+3)/(4) = (z+1)/(1) are mutually perpendicular.

Show that the lines (x-3)/(2)=(y+1)/(-3) =(z-2)/(4) " and " (x+2)/(2) =(y-2)/(4) =(z+5)/(2) are perpendicular to each other .

If the lines (x -1)/(-3) = (x - 2)/(2k) = (z - 3)/(2) and (x - 1)/(3k ) = (y -1)/(1) = (z - 6)/(-5) are perpendicular to each other, then the value of k is ,

Show that the lines : (x + 1)/(3) = (y + 3)/(5) = (z + 5)/(7) and " " (x -2)/(1) = (y - 4)/(3) = (z -6)/(5) intersect each other. Also, find the their point of intersection.

Show that the lines : (i) (x -5)/(7) = (y + 2)/(-5) = (z)/(1) " " and (x)/(1) = (y)/(2) = (z)/(3) (ii) (x - 3)/(2) = (y + 1)/(-3) = (z - 2)/(4) and (x + 2)/(2) = (y - 4)/(4) = (z + 5)/(2) are perpendicular to each other .

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

The value of alpha for which the lines (x-1)/(2)=(2y-1)/(3)=(1-3z)/(alpha) and (x+1)/(2)=(3y-5)/(2)=(z-4)/(3) are perpendicular to each other is

Prove that the lines 3x + 2y + z – 5 = 0 = x + y – 2z – 3 and 2x – y – z = 0 = 7x + 10y – 8z – 15 are perpendicular

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

MODERN PUBLICATION-THREE DIMENSIONAL GEOMETRY -EXERCISE 11 (E) (SHORT ANSWER TYPE QUESTIONS )
  1. (i) Find the distance from (1,2,3 ) to the plane 2x + 3y - z + 2 = 0 ....

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  2. Find the angle between the planes : (i) 3 x - 6y - 2z = 7 " " ...

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  3. Angle between the planes: (i) vec(r). (hati - 2 hatj - hatk) = 1 and ...

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  4. (i) The position vectors of two points A and B are 3 hati + hatj + 2 h...

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  5. Find the equation of the plane passing through the point (1,2,1) and p...

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  6. Find the vector and Cartesian equations of the plane which passes thro...

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  7. Find the vector and cartesian equation of the plane : (i) that passe...

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  8. Find the length of the perpendicular from the point (2,3,7) to the pla...

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  9. In the following, find the distance of each of the given points from t...

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  10. In the following, determine the direction-cosines of the normal to the...

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  11. If the points (1," "1," "p)" "a n d" "(" "3," "0," "1) be equidistant ...

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  12. In the following cases, find the co-ordinates of the foot of the perpe...

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  13. Find the length and the foot of the perpendicular from the point P(7,1...

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  14. (i) Find the vector equation of the line passing through (1,2,3) and p...

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  15. (i) Find the equations of the plane passing through (a,b,c) and parall...

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  16. Find the vector and catesian equations of the plane containing the lin...

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  17. Find the angle between the lines x-2y+z=0=x+2y-2za n dx+2y+z=0=3x+9y+5...

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  18. Show that the line 3x - 2y + 5 = 0 , y + 3z - 15 = 0 and (x -1)/(5) =...

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  19. Find the equations of the line passing through the point (1, -2, 3) an...

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  20. Find the equation of the plane which bisects the line segment joining ...

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