Question

Which Cartesian equation is obtained for the line through \[(5,2,-4)\] parallel to \[3\hat{i}+2\hat{j}-8\hat{k}\]?

Options

• \[\frac{x-5}{3}=\frac{y-2}{2}=\frac{z+4}{-8}\]

• \[\frac{x-5}{-3}=\frac{y-2}{-2}=\frac{z+4}{8}\]

• \[\frac{x+5}{3}=\frac{y+2}{2}=\frac{z-4}{-8}\]

• \[\frac{x-5}{5}=\frac{y-2}{2}=\frac{z+4}{-4}\]

Answer 1

Substitution gives \[x_1=5\], \[y_1=2\], \[z_1=-4\] and \[a=3\], \[b=2\], \[c=-8\]. Since \[z-z_1=z-(-4)\], the third numerator is \[z+4\].