Recall that in the symmetrical form of a line, coefficients of x, y and z are unity. Therefore, to put the given line in a symmetric form, we must make the coefficients of x, y and z as unity. The given line is
his shows that the given line passes through (1/3, −1/3, 1), and has direction ratios 1, 2 and 3. In vector form, this means that the line passes through the point having position vector a = 1/3i - 1/3j + k and is parallel to the vector b = i + 2j + 3k.
Therefore, its vector equation is
vector r = (1/3i - 1/3j + k) + λ(i + 2j + 3k)
