Show that the line vecr=hati+hatj+lambda...

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

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Find the distance of the point (-1, -5, -10) from the point of intersection of the line vecr=2hati-hatj+2hatk+lambda(3hati+4hatj+2hatk) and the plane vecr.(hati-hatj+hatk)=5

The angle between the line vecr=(5hati-hatj-4hatk)+lambda(2hati-hatj+hatk) and the plane barr.(3hati-4hatj-hatk)+5=0 is sin^(-1)((5)/(2sqrt(91))) .

Find the shortest distance between the lines vecr=(4hati-hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk) .

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 shortest distance between lines vecr=6hati+2hatj+2hatk+lambda (hati-2hatj+2hatk) and vecr=-4hati-hatk+mu(3hati-2hatj-2hatk).

Find the shortest distance between the lines l_1 and l_2 whose vector equations are vecr=hati+hatj+lambda(2hati-hatj+hatk) and vecr=2hati+hatj-hatk+mu(3hati-5hatj+2hatk).

Show that the vectors 2hati-3hatj+4hatk and -4hati+6hatj-8hatk are collinear.

Find the angle between the following pairs of lines : (i) vecr=2hati-5hatj+hatk+lambda(3hati+2hatj+6hatk) and veck=7hati-6hatk+mu(hati+2hatj+2hatk) (ii) vecr=3hati+hatj-2hatk+lambda(hati-hatj-2hatk) and vecr=2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)

Find the vector equation of the plane containing the lines vecr=(hati+hatj-hatk)+lambda(3hati-hatj) and vecr=(4hati-hatk)+mu(2hati+3hatk) .

Show that the vectors, vec(a)=hati-2hatj+3hatk,vec(b)=-2hati+3hatj-4hatk and vec( c )=hati-3hatj+5hatk are coplanar.

KUMAR PRAKASHAN-THREE DIMENSIONAL GEOMETRY-PRACTICE WORK

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Show that the line vecr=hati+hatj+lambda(2hati+hatj+4hatk) lies in the...
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Find the image of the point (1, 3, 4) in the plane vecr.(2hati-hatj+ha...
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