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A set of D.R of the line vecr=(hati+hatj...

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

A

`lt1,1,1gt`

B

`lt2,3,6gt`

C

`lt2hati,3hatj,6hatkgt`

D

none of these

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Find the point of intersection of the line : vecr=(hati+2hatj+3hatk)+lambda(2hati+hatj+2hatk) and the plane vecr*(2hati-6hatj+3hatk)+5=0 .

Write the equation of the following line vecr=hati+hatj+hatk+t(2hati-3hatj+6hatk) , t in R. in the cartestian form.

Find the vector and Cartesian form of the equation of the plane passing through the point (1, 2, -4) and parallel to the lines vecr=hati+2hatj-4hatk+lamda(2hati+3hatj+6hatk) and vecr=hati-3hatj+5hatk+mu(hati+hatj-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 angle between the line vecr=(hati+hatj+hatk)+lambda(2hati-hatj-hatk) and the plane vecr.(hati+hatj-2hatk) =3.

Find the shortest distance between the lines vecr = (hati + 2hatj+hatk) + lambda(hati-hatj+hatk) and vecr = 2hati - hatj-hatk + mu(2hati+hatj+2hatk)

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.

Find the equation of the line passing through the point (1,2,-3) and perpendicular to the lines : vecr=(2hati-hatj-hatk)+lambda(2hati-hatj-3hatk) and vecr=(3hati-hatj-2hatk)+mu(hati+hatj+hatk)

Find the equation in vector anf cartesian form of the line passing through the point : (2,-1,3) and perpendicular to the lines vecr= (hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr= (2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) .

Find the equation of the line passing through the point (2, -1, 3) and perpendicular to the lines : vecr=(hati-hatj+hatk)+lambda(2hati+hatj-3hatk) and vecr=(hati+hatj-hatk)+mu(hati+hatj+hatk)

PRADEEP PUBLICATION-THREE DIMENSIONAL GEOMETRY-EXERCISE
  1. If a line makes angles alpha,beta,gamma respectively with positive dir...

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

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

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

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

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

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

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

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  9. The area of the quadrilateral ABCD, where A 0,4, 1), B (2, 3, -1), C (...

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  10. The line x=1, y=2 is

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  11. The distance between the planes 3x+2y-6z=14=0 and 3x+2y-6z+21=0 is

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  12. The line (x-x1)/0=(y-y1)/1=(z-z1)/2 is

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  13. The line (x-x1)/0=(y-y1)/1=(z-z1)/2 is

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  14. The locus represented by x y + yz=0 is

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  15. The line (x-x1)/a=(y-y1)/b=(z-z1)/c is at right angles to the plane Ax...

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  16. The line (x-x1)/a=(y-y1)/b=(z-z1)/c is parallel to the plane Ax+By+Cz+...

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  17. The lines vecr=a1+tvecv1 and vecr=a2+svecv2 lie in a plane (vecv1xxvec...

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  18. If the projections of vec(PQ) on OX, OY and OZ are respectively 12,4,a...

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  19. The reflection of the point (alpha,beta,gamma) in the xy-plane is:

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  20. The projection of the point (1,2,-4) in the YOZ-plane is

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