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find the vector equations of the line which is parallel to the vector `3hati-2hatj+6hatk` and which is passes through the point (1,-2,3)

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Find the vector equation of the line which is parallel to the vector 3hati-2hatj+hatk and which passes through the point (1,-2,3).

Find the direction cosines of the vectors: 6hati-2hatj-3hatk

Find the projection of the vector hati+3hatj+7hatk on the vector 2hati-3hatj+6hatk .

Find the vector equation of the line through the origin, which is perpendicular to the plane vecr*(hati-2hatj+hatk)=3 .

Find the vector equation of the line through (4,3,-1) and parallel to the line: vecr=(2hati-hatj+3hatk)+lambda(3hati-hatj+4hatk)

Find the vector equation of the plane through the planes : vecr*(hati+hatj+hatk)=6 and vecr*(2hati+3hatj+4hatk)=-5 at the point (1,1,1).

Find a vector of magnitude 7 , which is perpendicular to both the vectors : 2hati-hatj+hatk and hati+hatj-hatk

Find a vector of magnitude 8, which is perpendicular to both the vectors 2hati-hatj+3hatk and -hati+2hatj-hatk .

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector 3hati + 2hatj - 2hatk

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. Write down the coordinates of the mid point of the segment joining the...

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  2. If the direction ratios of a line <2,-1,-2> find the direction cosines...

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  3. find the vector equations of the line which is parallel to the vector ...

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  4. Find the direction cosines of the line passing through the points P(2,...

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  5. If a line makes an angles of 30^@, 60^@, 90^@ with the positive direct...

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  6. If the x - coordinate of a point P on the line joining points Q(2,2,1)...

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  7. Find the distance of the point whose position vector is 2hati+hatj-hat...

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  8. Find the position vector of a point A in space such thatvec(OA) is inc...

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  9. Parametric equations of a line are x=-1+2t, y=3-4t and z=2+t. find the...

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  10. Parametric equations a line are x=2-3t, y=-1+2t and z=3+t. write down ...

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  11. Vector equations of a line if vecr=3hati-6hatj+7hatk+lambda(2hati-hatj...

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  12. Vector equation of a plane is vecr.(2hati+4hatj-3hatk)=5. Write down t...

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  13. What is the distance of the point (-1,2,1) from the plane 2x-3y+4z+5=0...

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  14. Find p if the plane x+y-2z+6=0 is parallel to the plane px+3y-6z-1=0.

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  15. Write the equation to the locus of a point which is always at a fixed ...

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  16. Find the vector equations to the locus of a point whose distance from ...

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  17. If the line drawn from the point (-2,-1,-3) meets a plane at right ang...

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  18. Write the distance of the plane 2x-y+2z+1=0 from the origin.

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  19. Write the direction of cosines of the line joining the poidnts (1,0,0)...

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  20. Write the vector equations of the plane throught the point (a,b,c) and...

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