Question

What is the parametric form of the line through \[(5,2,-4)\] with direction ratios \[3,2,-8\]?

Options

• \[x=5+3\lambda,\quad y=2+2\lambda,\quad z=-4-8\lambda\]

• \[x=3+5\lambda,\quad y=2+2\lambda,\quad z=-8-4\lambda\]

• \[x=5+3\lambda,\quad y=2-2\lambda,\quad z=-4+8\lambda\]

• \[x=5-3\lambda,\quad y=2-2\lambda,\quad z=-4+8\lambda\]

Answer 1

Use \[x=x_1+\lambda a\], \[y=y_1+\lambda b\], and \[z=z_1+\lambda c\]. Here, \[z=-4+\lambda(-8)=-4-8\lambda\].