Find the equation of a line which passes through a given point of position vector `vec c` and is parallel to a given vector `vecb`.

Find the equation of a line through a point C of position vector vec c=3veci+2vecj and perpendicular to the vector vecb=veci-vecj in the xy-plane.

Find the vector equation of a lin e passes through the point whose position vector is (2hati-hatj-hatk) and parallel to vector hati+5hatk .

Equation of line passing through a given point and parallel to given line

Find the equation of line which passes through a point (-1, 2, 3) and is parallel to a vector having direction ratios (3, 4, 2).

Show that equation of the plane passing through a point having position vector vec(a) and parallel to vec(b) and vec(c) is vec(r) = vec(a) + lambda vec(b) + mu vec(c) .

Find the vector equation of a line which passes through the point with position vector 4hati - hatj + 2 hatk and is in the direction of - 2 hati + hatj + hatk .

Find the vector equation of the line which passes through the point with position vector 4hati - hatj + 2 hat k and is in the direction of - 2hati + hatj + hat k .

Find the vector equation of a line passing through a point with position vector 2hat i-hat j+hat k ,and parallel to the line joining the points -hat i+4hat j+hat k and hat i+2hat j+2hat k. Also, find the cartesian equivalent of this equation.

Equation of line passing through a given point and perpendicular to given line

Find the vector equation of the line passing through the point with position vector 2 hati - hatj + hatk and parallel to the line joining the points with position vectors - hati + 4hatj + hatk and hati + 2 hatj + 2 hatk . Also, find the cartesian equation of the line.