A line passes through (2, −1, 3) and is perpendicular to the lines `vecr=(hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr=(2hati-hatj-3hatk)+mu(hati+2hatj+2hatk)` . Obtain its equation in vector and Cartesian from.
Since the line passes through a point (2,-1,3), its equation will be
The normal vector of this line is `Ahati+Bhatj+Chatk.`
Since this line is perpendicular to the two given lines, the dot product of their respective normals will be 0.
Adding (1) and (2), we get:
Substituing in (1), we get `B=A/2.`
Substituting the values of B and C in the equation of the line, we get:
is the required equation of the line.