Find the shortest distance between the l...

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

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Find the angle between the vector 2 hati+ 3hatj+ hatk and 2 hati - hatj- hatk .

Find the measure of the angle between the vectors 3 hati + 2 hatj + 2hatk and 2 hati - hatj - 2 hatk .

What is the angle between vectors veca = hati - hatj + hatk and vecb = hati + hatj - hatk ?

Find the shortest distance between the lines (vecr = 6veci+2vecj+2veck+lambda(veci-2vecj+2veck) and vecr = -4veci-veck+mu(3veci-2vecj+2veck) .

Find unit vectors perpendicular to the vectors 2hati - 3hatj + 4hatk and 4hati - hatj - 2hatk .

Find the acute angle between the planes whose vector equations are vecr. (2 hati + 2 hatj - 3 hatk)= 5 and vecr. (3 hati - 3 hatj + 5 hatk) = 3.

Find the angle between the planes whose vector equation are given by vecr. (2 hati - hatj + 3 hatk) = 4 and vecr . (hati - 2 hatj + 4 hatk) =1.

If vecu= 2hati-hatj+hatk, vecv = hati + 2 hatj-3 hatk and vecw= 3hati + phatj+ 5 hatk are coplanar find the value of p.

Find the unit vector in the direction of the vector veca+vecb where veca =2hati - hatj +2 hatk and vecb = - hatj +hatj- hatk

Find lambda if the vectors veca = 2hati - hatj+ hatk , vecb = hati + 2hatj - 3hatk and vecc =3 hati + lambdahatj+5 hatk are coplanar.