Question

Which parametric form corresponds to a line through \[A(x_1,y_1,z_1)\] with direction ratios \[a,b,c\]?

Options

• \[x=x_1+\lambda a,\quad y=y_1+\lambda b,\quad z=z_1+\lambda c\]

• \[x=x_1+\lambda x,\quad y=y_1+\lambda y,\quad z=z_1+\lambda z\]

• \[x=x_1+\lambda b,\quad y=y_1+\lambda c,\quad z=z_1+\lambda a\]

• \[x=a+\lambda x_1,\quad y=b+\lambda y_1,\quad z=c+\lambda z_1\]

Answer 1

Each coordinate begins with the corresponding coordinate of \[A(x_1,y_1,z_1)\]. The additions use the corresponding direction ratios \[a,b,c\] with the same parameter \[\lambda\].