The line `vecr=hati+hatj-hatk+lamda(3i-j) and vecr.=4hati-hastk+mu(2hati+3hatk)` interset at the point (A) (0,0,0) (B) (0,0,1) (C) (0,-4-1) (D) (4,0,-1)

The lines vecr=(hati+hatj)+lamda(hati+hatk)andvecr=(hati+hatj)+mu(-hati+hatj-hatk) are

Show that the lines vecr= hati+hatj-hatk+lambda(3hati-hatj) and vecr = 4 hati+hatk+mu(2hati+3hatk) intersect. Also find the co[-ordinates of their point of intersection.

The angle between the line vecr=(hati+2hatj+3hatk)=lamda(2hati+3hatj+4hatk) and the plane vecr.(hati+2hatj-2hatk)=3 is (A) 0^0 (B) 60^0 (C) 30^0 (D) 90^0

The distance of the line vecr=2hati-2hatj+3hatk +lamda(hati-2hatj+4hatk) and the plane vecr.(hati+5hatj+hatk)=5 is (A) 10/3 (B) (1,-2) (C) 10/(3sqrt(3)) (D) 10/9

The equation of the plane containing the lines vecr=(hati+hatj-hatk)+lamda(3hati-hatj) and vecr=(4hati-hatk)+mu(2hati+3hatk) , is

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

Find the shortest distance between the following lines : (i) vecr=4hati-hatj+lambda(hati+2hatj-3hatk) and vecr=hati-hatj+2hatk+mu(2hati+4hatj-5hatk) (ii) vecr=-hati+hatj-hatk+lambda(hati+hatj-hatk) and vecr=hati-hatj+2hatk+mu(-hati+2hatj+hatk) (iii) (x-1)/(-1) = (y+2)/(1) = (z-3)/(-2) and (x-1)/(1) = (y+1)/(2) = (z+1)/(-2) (iv) (x-1)/(2) = (y-2)/(3) = (z-3)/(4) and (x-2)/(3) = (y-3)/(4) = (z-5)/(5) (v) vecr = veci+2hatj+3hatk+lambda(hati-hatj+hatk) and vecr = 2hati-hatj-hatk+mu(-hati+hatj-hatk)

If the planes vecr.(2hati-hatj+2hatk)=4 and vecr.(3hati+2hatj+lamda hatk)=3 are perpendicular then lamda=

Show that the line vecr = (hati+hatj-hatk)+lambda(3hati-hatj) vecr = (4hati-hatk)+mu(2hati+3hatk) are coplanar. Also find the equation of plane in which these lines lie.