Given:
[tex]L:\frac{x+10}{2}=y=\frac{z-1}{3}[/tex]
Required:
We need to find the point that lies on the given line and director vector.
Explanation:
Consider the equation.
[tex]\frac{x+10}{2}=y[/tex]
Set x =2 and substitute in the equation.
[tex]\frac{2+10}{2}=y[/tex][tex]\frac{12}{2}=y[/tex][tex]6=y[/tex]
We get y =2
Consider the equation.
[tex]y=\frac{z-1}{3}[/tex]
Substitute y =6 in the equation.
[tex]6=\frac{z-1}{3}[/tex]
Multiply both sides by 3.
[tex]3\times6=3\times\frac{z-1}{3}[/tex][tex]18=z-1[/tex]
Add 1 to both sides.
[tex]18+1=z-1+1[/tex][tex]19=z[/tex]
We get z =19.
The given line passes through the point ( 2,6,19).
[tex]\text{ Set x =0 in the equation }\frac{x+10}{2}=y.[/tex][tex]\frac{10}{2}=y[/tex][tex]5=y[/tex]
[tex]\text{ Set y =0 in the equation }\frac{x+10}{2}=y.[/tex][tex]\frac{x+10}{2}=0[/tex][tex]x=-10[/tex]
[tex]Set\text{ y =0 in the equation }y=\frac{z-1}{3}.[/tex][tex]\frac{z-1}{3}=0[/tex][tex]z-1=0[/tex][tex]z=1[/tex]
The director vector is (-10, 5.1).
Final answer:
The given line passes through the point ( 2,6,19).
The director vector is (-10, 5.1).
