Show that the line L whose vector equati...

Show that the line L whose vector equation is `vecr=2hati-2hatj+3hatk+lambda(hati-hatj+4hatk) ` is parallel to the plane `pi` whose vector equation is `vecr*(hati+5hatj+hatk)=5` and find the distance between them.

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Show that the plane whose vector equation is vecr.(hati+2hatj-hatk)=3 contains the line whose vector equation is vecr=hati+hatj+lambda(2hati+hatj+4hatk) .

State when the line vecr=veca+lambdavecb is parallel to the plane vecr*vecn=d . Show that the line vecr=hati+hatj+lambda (2hati+hatk+4hatk) is parallel to the plane vecr*(-2hati+hatk)=5 . Also, find the distance between the line and the plane.

Show that the line , vecr=2hati-3hatj+5hatk+lambda(hati-hatj+2hatk) lies in the plane vecr*(3hati+hatj-hatk)+2=0 .

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)

Show that the line , vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the plane vecr*(hati+2hatj-hatk)=3 .

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

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

Show that the lines vecr=hati+hatj+hatk+lambda(hati-hatj+hatk) and vecr=4hatj+2hatk+mu(2hati-hatj+3hatk) are coplanar.

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

MODERN PUBLICATION-Three Dimensional Geometry-EXERCISE

Find the co-ordinates of the foot of the perpendicular from the point(...
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State when the line vecr=veca+lambdavecb is parallel to the plane vecr...
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Find the length of the perpendicular from the point (1,2,3) to the lin...
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Show that the points (2, 3, 4), (– 1, – 2, 1), (5, 8, 7) are collinear...
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Find the direction cosines of the sides of the triangle whose vertices...
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show that the three lines with direction cosines <12/13,-3/13,-4/13>, ...
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