Find the distance of the point (1, -2, 9) from the point of intersection of the line `vec(r)= 4hat(i)+ 2hat(j) + 7hat(k) + lamda (3hat(i) + 4hat(j) + 2hat(k))` and the plane `vec(r). (hat(i)- hat(j) +hat(k))= 10`

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.

Find the distance of the point (-1,-5,-10) from the point of intersection of the line vec r=2hat i-hat j+2hat k+lambda(3hat i+4hat j+2hat k) and the plane vec r*(hat i-hat j+hat k)=5

Find the distance of the point (-1,-5,-10), from the point of intersection of the line vec r=(2hat i-hat j+2k)+lambda(3hat i+4hat j+2hat k) and the plane vec r.(hat i-hat j+hat k)=5

Find the distance of the point (-1,-5,-10) from the point of intersection of line vec r=2hat i-hat j+2hat k+lambda(3hat i+4hat j+2hat k) and the plane vec r*(hat i-hat j+hat k)=5

find the distance between (-1,-5,-10) from the point of intersection of the line vec r=2hat i-hat j+2hat k+lambda(3hat i+4hat j+2hat k) and the plane vec r*(hat i-hat j+hat k)=5

The point of intersection of the lines vec(r) = 7hat(i) + 10 hat(j)+ 13 hat(k) , vec(s) = (2hat(i) + 3hat(j)+4hat(k)) and vec(r) = 3hat(i) + 5hat(j) + 7hat(k) + t(hat(i) + 2hat(j) + 3hat(k)) is

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

Find the distance of the point with position vector -hat i-5 hat j-10 hat k from the point of intersection of the line vec r=(2 hat i- hat j+2 hat k)+lambda(3 hat i+4 hat j+12 hat k) with the plane vec rdot(( hat i- hat j+ hat k)=5.

Find the angle between the line: vec(r) = (hat(i) - hat(j) + hat(k) ) + lambda (2 hat(i) - hat(j) + 3 hat(k)) and the plane vec(r). (2 hat(i) + hat(j) - hat(k) ) = 4. Also, find the whether the line is parallel to the plane or not.