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

For the plane vec(r).(2hat(i)+3hat(j)+5hat(k))=3

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.

Find the angle between the planes vec(r)*(hat(i)+hat(j)-2hat(k))=3and2x-2y+z=2

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= 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.

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 non-parametric form of vector equation, and Cartesian equations of the plane vec(r)=(6hat(i)-hat(j)+hat(k))+s(-hat(i)+2hat(j)+hatk)+t(-5hat(j)-4hat(j)-5hat(k))

Find the angle between the vectors hat i - 2 hat j + 3 hat k and 3 hat i - 2 hat j + hat k .