If the lines vec(r) = (hat(i) - hat(j) +...

If the lines `vec(r) = (hat(i) - hat(j) + hat(k)) + lambda (3 hat(j) - hat(k)) and vec(r ) = (alpha hat(i)-hat(j))+mu (2 hat(i) - 3 hat(k))` are co planar , then the distance of the plane containing these two lines from the point `(alpha , 0 , 0)` is :

`2/9`

`2/11`

`4/11`

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vec(r )=(-4hat(i)+4hat(j) +hat(k)) + lambda (hat(i) +hat(j) -hat(k)) vec(r)=(-3hat(i) -8hat(j) -3hat(k)) + mu (2hat(i) +3hat(j) +3hat(k))

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.

Show that the lines vec(r ) =(hat(i) -hat(j)) +lambda (2hat(i)+ hat(k)) " and " vec(r ) =(2hat(i) -hat(j)) + mu (hat(i)+ hat(j) -hat(k)) do not intersect .

Show that the lines vec(r) =(hat(i) +2hat(j) +hat(k)) +lambda (hat(i)-hat(j)+hat(k)) " and " vec(r ) =(hat(i) +hat(j) -hat(k)) + mu (hat(i)- hat(j) + 2hat(k)) Do not intersect .

vec(r ) =(3hat(i) -4hat(j) +2hat(k)) + lambda (hat(i)+3hat(k)) " and " vec(r ) = 5hat(i) + mu (-hat(i) +hat(j) + hat(k)) Find angle between the lines .

If vec(r) = (hat(i) + 2hat(j) + 3hat(k)) + lambda(hat(i) - hat(j) + hat(k)) and vec(r) = (hat(i) + 2hat(j) + 3hat(k)) + mu (hat(i) + hat(j) - hat(k)) are two lines, then find the equation of acute angle bisector of two lines.

Find the equation of the line perpendicular to the lines : vec(r) = ( 3 hat(i) + 2 hat(j) - 4 hat(k)) + lambda (hat(i) + 2 hat(j) - 2 hat(k)) and vec(r) = (5 hat(j) - 2 hat(k) + mu (3 hat(i) + 2 hat(j) + 6 hat(k) ) and passing through the point (1,1,1) .

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