The co-ordinate of the point P on the line `r=(hat(i)+hat(j)+hat(k))+lambda(-hat(I)+hat(j)-hat(k))` which is nearest to the origin is

The coordinates of the point P on the line vec r=( hat i+ hat j+ hat k)+lambda(- hat i+ hat j- hat k) which is nearest to the origin is

Find the point of intersection of the line : vec(r) = (hat(i) + 2 hat(j) + 3 hat(k) ) + lambda (2 hat(i) + hat(j) + 2 hat(k)) and the plane vec(r). (2 hat(i) - 6 hat(j) + 3 hat(k) ) + 5 = 0.

The angle between the line r=(hat(i)+2hat(j)-hat(k))+lamda(hat(i)-hat(j)+hat(k)) and the plane r*(2hat(i)-hat(j)+hat(k))=4 is

A point on the line hat r=2hat i+3hat j+4hat k+t(hat i+hat j+hat k) is

A point on the line vec r=2hat i+3hat j+4hat k+t(hat i+hat j+hat k) is

Find the vector and cartesian equations of a plane containing the two lines vec(r) = (2 hat(i) + hat(j) - 3 hat(k)) + lambda(hat(i) + 2 hat(j) + 5 hat(k)) and vec(r) = (3hat(i) + 3 hat(j) + 2 hat(k)) + lambda (3 hat(i) - 2 hat(j) + 5 hat(k)) . Also show that the line vec(r) = (2 hat(i) + 5 hat(j) + 2 hat(k)) + p (3 hat(i) - 2 hat(j) + 5 hat(k)) lies in the plane.