Conditions for line to intersect

Two lines intersect

Condition for a line to lie in a plane

Condition of line to be parallel perpendicular and intersecting

The condition for intersecting the lines vec(r)=vec(a)_(1)+tvec(b)_(1) and vec(r)=vec(a)_(2)+svec(b)_(2) is

Read the graph carefully: Write the algebraic condition, when two lines are intersecting lines.

Condition of intersection of line and ellipse

Find the condition that the lines vec r=vec a+t(vec b xxvec c),vec r=vec b+p(vec c xxvec a) may intersect.Accepting that condition,find the point of intersection.

Find the condition for the lines joining the origin to the points of intersection of the circle x^2+y^2=a^2 and the line lx+my=1 to coincide.

Find the condition for which the lines joining the origin to the points of intersection of the line y= mx+c and the circle x^2+y^2=a^2 will be mutually bot

Find the condition for the lines joining the originto the points of intersection of the circle x^2 + y^2 = a^2 and the line lx + my = 1 to coincide.