[" Show that the lines "],[qquad [vec r,=hat i+hat j-hat k+lambda(3hat i-hat j)],[" and ",vec r=4hat i-hat k+mu(2hat i+3hat k)" intersect "]]

Show that the lines vec r=(hat i+hat j-hat k)+lambda(3hat i-hat j) and vec r=(4hat i-hat k)+mu(2hat i+3hat k) are coplanar.Also,find the plane containing these two lines.

Show that the lines vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d vec r=(4 hat i- hat k)+mu(2 hat i+3 hat k) are coplanar. Also, find the plane containing these two lines.

Statement 1: Lines vec r=hat i+hat j-hat hat k+lambda(3hat i-hat j) and vec r=4hat i-hat k+mu(2hat i++3hat k) intersect.Statement 2:vec b xxvec d=0, then lines vec r=vec a+lambdavec b and vec r=vec c+lambdavec d do not intersect.

Statement 1: Lines vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j)a n d vec r=4 hat i- hat k+mu(2 hat i++3 hat k) intersect. Statement 2: vec bxx vec d=0 , then lines vec r= vec a+lambda vec ba n d vec r= vec c+lambda vec d do not intersect.

Statement 1: Lines vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j)a n d vec r=4 hat i- hat k+mu(2 hat i++3 hat k) intersect. Statement 2: vec bxx vec d=0 , then lines vec r= vec a+lambda vec ba n d vec r= vec c+lambda vec d do not intersect.

Statement 1: Lines vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j)a n d vec r=4 hat i- hat k+mu(2 hat i+3 hat k) intersect. Statement 2: vec bxx vec d=0 , then lines vec r= vec a+lambda vec ba n d vec r= vec c+lambda vec d do not intersect.

Show that the lines vec( r) =(hat(i) +hat(j) -hat(k)) +lambda (3hat(i) -hat(j)) " and " vec( r) =(4hat(i) -hat(k)) + mu (2hat(i) +3hat(k)) intersect . Find the point of the intersection.

Determine the shortest distance between the pair of lines : vec r=( hat i+ hat j- hat k)+lambda(3 hat i- hat j)a n d\ vec r=(2 hat i- hat k)+mu(2 hat i+2 hat k)dot

vec r=(4hat i-hat j)+lambda(hat i+2hat j-3hat k) and vec r=(hat i-hat j+2hat k)+mu(2hat i+4hat j-5hat k)

The lines vec(r)=hat(i)+hat(j)-hat(k)+lamda(3hat(i)-hat(j)) and vec(r)=(4hat(i)-hat(k))+mu(2hat(i)+3hat(k)) -