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Find the vector equation of plane that p...

Find the vector equation of plane that passes through the point (1,0,-2) and the normal to the plane is `hat(i)+hat(j)-hat(k)`.

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Find the eqution of a line which is passes through the point (1,1,1) and parallel to 2hat(i)+hat(j)-3hat(k) .

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Find the vector equation of the plane passing through the intersection of the planes vec(r)*(2hat(i)+2hat(j)-3hat(k))+7=0 and vec(r)*(2hat(i)+5hat(j)+3hat(k))=9 and passing through the point (2,1,3).

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Find the equation of the straight line passing through the point (2,-1,3) and perpendicular to the lines vec(r)=(hat(i)+hat(j)-hat(k))+lamda(2hat(i)+hat(j)-3hat(k)) and vec(r)=(hat(i)-hat(j)-hat(k))+mu(hat(i)+hat(j)+hat(k)) .

Find the equation of plane passing through the point (1, 2, 3) and having the vector r=2hat(i)-hat(j)+3hat(k) normal to it.

OMEGA PUBLICATION-THREE DIMENSIONAL GEOMETRY -Questions
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  2. Find the angle between the planes whose vector equations are vec(r)(...

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  3. Find the vector equation of plane that passes through the point (1,0,-...

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  4. If a line has direction ratios -18,12,-4, then what are its direction ...

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  5. Find the direction cosines of the sides of the triangle whose vertices...

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  6. A line passes through the point with position vector 2hat(i)-hat(j)+4h...

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  7. Show that the line through the points : (4,7,8), (2,3,4) is parallel t...

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  8. Find the cartesian equation of the line which passes through the point...

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  9. The vector equation of the line (x-5)/(3)=(y+4)/(7)=(z-6)/(2) is ........

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  10. Find the vector and the cartesian equations of the line that passes th...

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  11. Find the angle between the pair of lines vec(r)=2hat(i)-5hat(j)+hat(...

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  12. Find the angle between the pairs of lines vec(r)=3hat(i)+hat(j)-2hat...

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  13. Find the angle between the pair of lines (x+3)/3 = (y-1)/5 = (z+3)/4an...

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  14. Find the angle between the pair of lines (x-2)/2=(y-1)/5=(z+3)/(-3) an...

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  15. Find the angle between the lines (x)/(2)=(y)/(2)=(z)/(1) and (x-5)/(4)...

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  16. Find the angle between the line (x+1)/2 = y/3 = (z-3)/6 and the plane ...

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  17. The vector equation of two lines are vec(r)=hat(i)+2hat(j)+hat(k)+la...

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  18. Find the shortest distance between the lines whose vector equations ar...

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  19. Find the shortest distance between the following two lines vec(r)=(1+2...

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  20. The vector equation of two lines are vec(r)=(1-t)hat(i)+(t-2)hat(j)...

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