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State true or False .The planes 2x +4y -...

State true or False .The planes `2x +4y -z + 1 = 0` and `x - 2y - 6z + 3 = 0` are perpendicular to each other.

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State True or False .The planes 2x - y + z -1 = 0 and 6x - 3y + 3z = 1 are coincident.

State with reasons which of following are true or false : The lines represented by 2x- 3y + 1 = 0 and 3x + 2y - k = 0 are perpendicular to each other for positive values of k only.

If the plane 2x+4y+z+2=0 and x-2y+kz+5=0 are perpendicular to each other what is the value of k ?

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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.

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USHA PUBLICATION-VECTORS THREE DIMENSIONAL GEOMETRY -EXERCISE
  1. The projection of a line segment axes are 3,4,12.Find the length and d...

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  2. Find the equation of the plane passing through the line x = y = z and ...

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  3. State true or False .The planes 2x +4y -z + 1 = 0 and x - 2y - 6z + 3 ...

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  4. Write the equation of the plane 3x-4y+z+5=0 in normal form.

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  5. Write the equation of the plane x+3y-7z+2=0 in the intercept from.

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  6. Find the equation of the plane passing through the point (2,3,1) and d...

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  7. Show that the ax+by+d =0 is perpendicular to xy-plane.

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  8. What are the direction cosines of the normal to the plane X+y+1=0?

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  9. Write the equation of the plane passing through (3,-6,-9) and parallel...

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  10. Write the equation of the plane passes through y-axis and z-axis.

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  11. What is the distance of the point (1,1,1)from the plane y=x?

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  12. Find the direction cosines of the line segment joining (3,6,1) and (4,...

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  13. What is the number of line which are equally inclined to the axes?

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  14. If the equation of x-axis is x/a=(y-d)/(b)=z/c, what is the value of a...

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  15. What are the direction cosines of the line (x-2)/(2)=(y+4)/(3)=(z-1)/6

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  16. Write the symmetrical from of the line X=5, y=4.

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  17. If the plane ax+by+cz=1 meets the co-ordinate axes at A,B,C, what is t...

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  18. If the points P(2,-1,1),Q(1,-3 c)and R(3,-4,-4) are the vertices of a ...

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  19. Show by vector method that the point P(3,-2, 4),Q(1,1 1)and R(-1,4,-2)...

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  20. If the vertices A,B,C of a triangle ABC are A(1,1,8),B(4,-3,-4)and C(-...

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