Find the acute angle between the following lines.
`vec(r)=(4hat(i)-hat(j))+t(hat(i)+2hat(j)-2hat(k))`
`vec(r)=(hat(i)-2hat(j)+4hat(k))+s(-hat(i)-2hat(j)+2hat(k))`

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

The angle between the lines vec(r)=(hat(i)+2hat(j)-3hat(k))+t(2hat(i)+hat(j)-2hat(k))" and the plane "vec(r)*(hat(i)+hat(j))+4=0 is

Find the acute angle between the following lines. (x+4)/(3)=(y-7)/(4)=(z+5)/(5),vec(r)=4hat(k)+t(2hat(i)+hat(j)+hat(k))

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 angel between the following pair of lines: vec r=2 hat i-5 hat j+ hat k+lambda(3 hat i+2 hat j+6 hat k)a n d vec r=7 hat i-6 hat k+mu( hat i+2 hat j+2 hat k) x/2=y/2=z/1a n d(x-5)/4=(y-2)/1=(z-3)/8

Find the angle between the line vec r= hat i+2 hat j- hat k+lambda( hat i- hat j+ hat k) and the plane vec rdot(2 hat i- hat j+ hat k)=4.

Find the parametric form of vector equation, and Cartesian equations of the plane containing the line vec(r)=(hat(i)-hat(j)+3hat(k))+t(2hat(i)-hat(j)+4hat(k))" and perpendicular to plane "vec(r)*(hat(i)+2hat(j)+hat(k))=8.

If vec(a)=vec(i)+2hat(j)+3hat(k),vec(b)=2hat(i)+hat(j)-2hat(k),vec(c)=3hat(i)+hat(2j)+hat(k)," find "vec(a)*(vec(b)xxvec(c))