The shortest distance between the skew lines `bar(r) = bar(a_(1)) + lamda bar(b_(1)) "and" bar(r) = bar(a_(2)) + mu bar(b_(2))` is

The shortest distance between the lines bar(r)=3bar(i)+5bar(j)+7bar(k)+lambda(bar(i)+2bar(j)+bar(k)) and bar(r)=-bar(i)-bar(j)+bar(k)+mu(7bar(i)-6bar(j)+bar(k)) is

Find the shortest distance between the skew lines . bar(r)=(6bar(i)+2bar(j)+2bar(k))+t(bar(i)-2bar(j)+2bar(k))andbar(r)=(-4bar(i)-bar(k))+s(3bar(i)-2bar(j)-2bar(k))

The shortest distance the two lines bar(r)=2bar(i)-bar(j)-bar(k)+lambda(2bar(i)+bar(j)+2bar(k)) and bar(r)=(bar(i)+2bar(j)+bar(k))+mu(bar(i)-bar(j)+bar(k)) is

Find the distance between the planes bar(r) * ( 2 bar(i) - bar(j) + 3 bar(k)) = 4 and bar(r) * ( 6 bar(i) - 3 bar(j) + 9 bar(k)) + 13 = 0

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

If the equation of two lines are given by bar(r)=bar(a_(1))+lamdabar(b_(1))andbar(r)=bar(a_(2))+mubar(b_(2)) , where lamda and mu are parmater , then the angle theta between the lines is

The distance between the line bar(r)=2bar(i)-2bar(j)+3bar(k)+lambda((bar(i)-bar(j)+4bar(k)) and the plane bar(r).(bar(i)+5bar(j)+bar(k))=5 is

If the line bar(r)=bar(a)+lamdabar(b) is parallel to the plane bar(r).bar(n)=p, then

If is the angle between plane bar(r).bar(n)=p and the line bar(r).bar(a)=lamdabar(b)