Find the angle between the lines `(x-1)/(2)=(y+1)/(3)=(z-4)/(6) and vecr=(-hati-2hatj+4hatk)+t(hatj+2hatk)`.

Find the shortest distance between the lines (x-6)/(3)=(y-7)/(-1)=(z-4)/(1) and vecr=-9hati+2hatk+t(-3hati +2hatj+4hatk) .

Find the angles between the planes vecr(hati-2hatj-2hatk)=1 and vecr(3hati-6hatj+2hatk)=0

The angles between the planes vecr.(3hati-6hatj+2hatk)=4 and vecr.(2hati-hatj+2hatk)=3 , is

Find the angle between the folowing planes :- (i) vecr.(2hati-3hatj+4hatk) = 5 and vecr.(-hati+hatj) = 1 (ii) vecr.(2hati+3hatj-6hatk) = 1 and vecr.(hati-2hatj+2hatk) + 3 = 0 (iii) x+y-2z=3 and 2x-2y+z+1 = 0 (iv) x+y-z=8 and -x+2y+z-1 = 0

Find the angle between the folowing planes :- (i) vecr.(2hati-3hatj+4hatk) = 5 and vecr.(-hati+hatj) = 1 (ii) vecr.(2hati+3hatj-6hatk) = 1 and vecr.(hati-2hatj+2hatk) + 3 = 0 (iii) x+y-2z=3 and 2x-2y+z+1 = 0

Find the angle between the following lines and the planes : (i) line vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk) and planes vecr.(2hati-hatj+hatk) = 4 . (ii) line vecr = (2hati+3hatj+9hatk)+lambda(2hati+3hatj+4hatk) and plane vecr.(hati+hatj+hatk) =5 . (iii) line (x+1)/(3) = y/2 = z/4 and plane 2x+y-3z=5 . (iv) line (x-3)/(9) = (y+4)/(6) = (z+2)/(2) and plane 3x-y+z=0 .

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

Find the angle between the following pairs of lines (i) veci=3hati+2hatj-4hatk+lambda(hati-2hatj+2hatk) and vecr=5hatj+hatk+mu(3hati+2hatj+6jhatk) (ii) vecr=hati+hatj+lambda(hati+2hatj+hatk) and vecr=mu(3hati+6hatj+4hatk) (iii) (x-1)/(2)=(y-2)/(3)-(z-1)/(-3) and (x+3)/(-1)=(y-5)/(8) = (z-1)/(4) (iv) (5-x)/(-2)=(y+3)/(-2)=(z-5)/(1) and (x+1)/(2) =(2y-3)/(4) = (z-2)/(1) (v) (x+3)/(1) = (y-1)/(2), z= 3 and (x-1)/(-2)=(y+3)/(3) = (z+5)/(4)

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 distance between the lines l_1 and l_2 given by vecr=hati+2hatj-4hatk+lambda(2hati+3hatj+6hatk) and vecr=3hati+3hatj-5hatk+mu(2hati+3hatj+6hatk)