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The angle between the lines vecr=(5hati-...

The angle between the lines `vecr=(5hati-hatj-4hatk)+lambda(2hati-hatj+hatk)` and the plane `vecr.(3hati-4hatj-hatk)+5=0` is `sin^-1(5/2sqrt91)`.

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Find the angle between the line vecr=(hati+hatj+hatk)+lambda(2hati-hatj-hatk) and the plane vecr.(hati+hatj-2hatk) =3.

Find the angle between the line vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk) and the plane vecr.(2hati-hatj+hatk)=4 .

Find the angle between the line vecr=(hati-hatj+3hatk)+lambda(2hati-hatj+hatk) and the plane vecr.(hati+hatj+2hatk) =4.

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Find the angle between the line : (2hati+3hatj+4hatk)+lambda(2hati+3hatj+4hatk) and the plane : vecr*(hati+hatj+hatk)=5 .

Find the angle between the line : vecr=(hati-hatj+hatk)+lambda(2hati-hatj+3hatk) and the plane vecr*(2hati+hatj-hatk)=4 . Also find whether the line is parallel to the plane or not.

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PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. The acute angle between the planes vecr.(2hati-3hatj+hatk)=1 and vecr....

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

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

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

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

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

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

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  8. Direction cosines of x-axis are

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

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

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

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

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

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

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

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

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

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  18. If alpha, beta, gamma are the angles that a line makes with the positi...

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  19. P is a point on the line segment joining the points (3, 2, -1) and (6,...

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  20. The shortest destance between vecr = veca1 + lambdavecb and vecr = vec...

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