Question

Consider the following line According to the information above, the line passes through the point and its director vector is

Answer 1

Given:

`L:(x+10)/(2)=y=(z-1)/(3)`

Required:

We need to find the point that lies on the given line and director vector.

Step-by-step explanation:

Consider the equation.

`(x+10)/(2)=y`

Set x =2 and substitute in the equation.

`(2+10)/(2)=y`
`(12)/(2)=y`
`6=y`

We get y =2

Consider the equation.

`y=(z-1)/(3)`

Substitute y =6 in the equation.

`6=(z-1)/(3)`

Multiply both sides by 3.

`3*6=3*(z-1)/(3)`
`18=z-1`

Add 1 to both sides.

`18+1=z-1+1`
`19=z`

We get z =19.

The given line passes through the point ( 2,6,19).

`\text{ Set x =0 in the equation }(x+10)/(2)=y.`
`(10)/(2)=y`
`5=y`

`\text{ Set y =0 in the equation }(x+10)/(2)=y.`
`(x+10)/(2)=0`
`x=-10`

`Set\text{ y =0 in the equation }y=(z-1)/(3).`
`(z-1)/(3)=0`
`z-1=0`
`z=1`

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).