Show that the lines vec(r)=(6hat(i)+hat(j)+2hat(k))+s(hat(i)+2hat(j)-3hat(k)),andvec(r)=(3hat(i)+2hat(j)-2hat(k))+t(2hat(i)+4hat(j)-5hat(k)) are skew lines and hence find the shortest distance between them.
Find the altitude of a parallelepiped determined by the vectors vec(a)=-2hat(i)+5hat(j)+3hat(k)" "vec(b)=hat(i)+3hat(j)-2hat(k)andvec(c)=-3hat(i)+hat(j)+4hat(k) if the base is taken as the parallelogram determined by vec(b)andvec(c).
If vec(a)=2hat(i)+3hat(j)-hat(k),vec(b)=hat(i)+2hat(j)-5hat(k),vec(c)=3hat(i)+5hat(j)-hat(k), then a vector perpendicular to vec(a) and lies in the plane containing vec(b)andvec(c) is
Find the angle between the line vec(r)=(2hat(i)-hat(j)+hat(k))+t(6hat(i)+2hat(j)-2hat(k))" and the plane "vec(r)*(6hat(i)+3hat(j)+2hat(k))=8