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True or false The vector equation of the...

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The vector equation of the line `(x-5)/3=(y+4)/7=(z-6)/2` is `vecr=5hati-4hatj+6hatk+lambda(3hati+7hatj+2hatk)`.

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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 and cartesian equations of the plane containing the lines: vecr=hati+2hatj-4hatk+lambda(2hati+3hatj+6hatk) and vecr=3hati+3hatj-5hatk+mu(-2hati+3hatj+8hatk) .

The vector equation of the line passing through the points (3,5, 4) and (5, 8, 11) is vecr=3hati+5hatj+4hatk+lamda(2hati+3hatj+7hatk)

Find the perpendicular distance from the point (1,2,3) to the line : vecr=6hati+7hatj+7hatk+lambda(3hati+2hatj-2hatk)

Find the shortest distance between two lines whose vector equations are : vecr=hati-7hatj-2hatk+lambda(hati+3hatj+2hatk) and vecr=-3hati+4hatj-2hatk+mu(-hati+2hatj+hatk)

Find the distance of the point with position vector -hati-5hatj-10hatk from the point of intersection of the line vecr=(2hati-hatj+2hatk)+lambda(3hati+4hatj+12hatk) and the plane vecr*(hati-hatj+hatk)=5 .

Find the shortest distance and the vector equation of the line of shortest distance between the lines given by : vecr= (3hati+8hatj+3hatk)+lambda(3hati-hatj+hatk) and vecr=(-3hati-7hatj+6hatk)+mu(-3hati+2hatj+4hatk) .

Find the shortest distance between two lines whose vector equations are : vecr=3hati+8hatj+3hatk+lambda(3hati-hatj+hatk) and vecr=-3hati-7hatj+6hatk+mu(-3hati+2hatj+4hatk)

Find the shortest distance between the lines whose vector equations are vecr = (hati+2hatj+3hatk) +lambda(hati-3hatj+2hatk) and vecr = 4hati+5hatj+6hatk+mu(2hati+3hatj+hatk)

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. The intercepts made by the plane 2 x – 3 y + 5z+4 = 0 on the co-ordina...

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  2. True or false The projection of the point (alpha,beta,gamma) on the z-...

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

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  4. The acute angle between the planes vecr.(2hati-3hatj+hatk)=1 and vecr....

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  5. If ltl,m,n,gtare D. cosines of a line then l^(2)+m^(2)+n^(2)=

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  6. The angle between the lines vecr=(5hati-hatj-4hatk)+lambda(2hati-hatj+...

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  7. True or false The distance of the point (-2,4,-5) from the line (x+3)/...

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  8. Find equation of a plane passing through the points (2,1,0),(3,-2,-2) ...

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  9. The equation of a line, which is parallel to 2hati+hatj+3hatk and whic...

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  10. True or false If the foot of perpendicular drawn from the origin to a ...

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  11. Direction cosines of x-axis are

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  12. Direction cosines of any normal to xy-plane are

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  13. Distance of the point (alpha, beta,gamma) from y-axis is

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  14. The distance of a point P(a,b,c) from x axis is:

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  15. If the direction cosine of a line are < k,k,k >, then,

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  16. If a line makes angles alpha,beta,gamma respectively with positive dir...

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  17. Distance of the point (alpha, beta,gamma) from y-axis is

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  18. The co-ordinates of foot of the perpendicular drawn from the point (2,...

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  19. The equation of x-axis is of the form

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  20. A set of D.R of the line vecr=(hati+hatj+hatk)+1(2hati+3hatj+6hatk)are

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