Find the parametric form of vector equation of a straight line passing through the point of intersection of the straight lines vecr=(hati+3hatj-hatk)+t(2hati+3hatj+2hatk) and (x-2)/(1)=(y-4)/(2)=(z+3)/(4) and perpendicular to both straight lines.

Find the parametric form of vector equation of the straight line passing through (-1,2,1) and parallel to the straight line vecr=(2hati+3hatj-hatk)+t(hati-2hatj+hatk) and hence find the shortest distance between the lines.

Form the differential equation of all straight lines touching the circle x^(2) +y^(2) =r^(2)

Form the differential equation of all straight lines touching the circle x^(2)+y^(2)=r^(2).

Find the differential equation for the family of all straight lines passing through the origin.

Find the differential equation for the family of all straight lines passing through the origin

Find the separate equations from a combined equation of a straight line 2x^(2)+xy-3y^(2)=0

Find the separated equations from a combined equation of a straight line 2x ^(2) + xy - 3y ^(2) =0

Form the differential equation satisfied by all the straight lines in xy - plane.

A straight line passes through the point (1,2,-3) and parallel to 4hati + 5hati - 7hatk . Find (i) vector equation in parametric form (ii) vector equation in non-parametric form (iii) Cartesian equation of the straight line.