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Show that the ax+by+d =0 is perpendicula...

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

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USHA PUBLICATION-VECTORS THREE DIMENSIONAL GEOMETRY -EXERCISE
  1. Write the equation of the plane x+3y-7z+2=0 in the intercept from.

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. 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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  17. If vec(a) makes equal angles with hat(i), hat(j) and hat(k) has magnit...

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  18. If abs(veca)=3,abs( vecb)=1,abs(vecc)=4 and veca+vecb+vecc=0,find the ...

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  19. Let hata,hatb,hatc be unit vectors. Suppose that and the angle between...

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  20. Calculate the area of the triangle ABC (by vector method) where A(1,1,...

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