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Show that the line barr=i+j+lambda(2i+j+...

Show that the line `barr=i+j+lambda(2i+j+4k)` is parallel to the plane `barr.(-2i+k)=5` .

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Find the distance between the line barr=i+j+lambda(2i+j+4k) and the plane barr.(-2i+k)=5 .

Consider a straight line through a fixed point with position vectors 2i-2j+3k and parallel to i-j+4k . Show that the straight line is parallel to the plane barr.(i+5j+k)=5

Consider a plane passing through the point (5,2,-4) and perpendicular to the line barr=(i+j)+lambda(2i+3j-k) Find its distance from the point (1,2,-1).

The angle between the line r = (i + 2j + 3k) + lambda (2i + 3j + 4k) and the plane r.(i + 2j -2k) = 0 is a) 0^(@) b) 60^(@) c) 30^(@) d) 90^(@)

Consider a plane passing through the point (5,2,-4) and perpendicular to the line barr=(i+j)+lambda(2i+3j-k) Find the angle made by it with line (x-1)/2=(y-2)/1=(z-3)/-2 .

The straight line r = (hat(i) + hat(j) + 2hat(k)) + t(2hat(i) + 5hat(j) + 3hat(k)) is parallel to the plane r.(2hat(i) + hat(j) - 3hat(k)) = 5 . Find distance between the straight line and plane

Find the shortest distance between the lines barr=i+j+lambda(2i-j+k) and barr=2i+j-k+mu(3i-5j+2k)

Consider a plane passing through the point (5,2,-4) and perpendicular to the line barr=(i+j)+lambda(2i+3j-k) Write the equation in Cartesian form.

The vector equation of the plane through the point (2,1,-1) and parallel to the plane r.(i+3j-k)=0 is a) r.(i+9j+11k)=6 b) r.(i-9j+11k)=4 c) r.(i+3j-k)=6 d) r.(i+3j-k)=4

Consider the line barr=(2i-j+k)+lambda(i+2j+3k) Write two points on the line obtained from vector equation of the line passing through A (1,0,2) and parallel to the line which are equidistant from A.

MAXIMUM PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXAMPLE
  1. Let the equation of a plane be barr.(2hati-3hatj+5hatk)=7, then find ...

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  2. State the condition of the line barr=bara+lambdabarb is parallel to th...

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  3. Show that the line barr=i+j+lambda(2i+j+4k) is parallel to the plane b...

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  4. Find the distance between the line barr=i+j+lambda(2i+j+4k) and the pl...

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  5. If a line in the space makes angle alpha,beta and gamma with the coord...

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  6. The direction ratios of the line (x-6)/1=(2-y)/2=(z-2)/2are a)6,-2,-2 ...

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  7. If the vector equation of a line is barr=i+j+k+mu(2i-3j-4k) , then t...

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  8. If the Cartesian equation of a plane is x+y+z=12 , then the vector equ...

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  9. Consider the lines barr=(i+2j-2k)+lambda(i+2j) and barr=(i+2j-2k)+mu...

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  10. Consider the lines barr=(i+2j-2k)+lambda(i+2j) and barr=(i+2j-2k)+mu...

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  11. Consider the lines barr=(i+2j-2k)+lambda(i+2j) and barr=(i+2j-2k)+mu...

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  12. Consider the line barr=(2i-j+k)+lambda(i+2j+3k). Find the Cartesian eq...

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  13. Consider the line barr=(2i-j+k)+lambda(i+2j+3k) Find the vector equa...

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  14. Consider the line barr=(2i-j+k)+lambda(i+2j+3k) Write two points on ...

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  15. Find the equation of the plane through the point (1,2,3) and perpendic...

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  16. Find the distance between the planes x-2y+2z-8=0 and 6y-3x-6z=57

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  17. Consider the Cartesian equation of line (x-3)/2=(y+1)/3=(z-5)/-2 Find...

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  18. Consider the Cartesian equation of line (x-3)/2=(y+1)/3=(z-5)/-2 F...

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  19. Consider the Cartesian equation of line (x-3)/2=(y+1)/3=(z-5)/-2 F...

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  20. From the following figure Find vec(AB)

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