Chapter 10.4, Problem 8E

(a)

To determine

To find:The set of parametric equations.

Answer to Problem 8E

Theparametric equations are $x=5+4t$ , $y=0$ and $z=10+3t$ .

Explanation of Solution

Given information:

The point is $\left(5,0,10\right)$ and vector is $v=4i+3k$ .

Formula used: The parametric equations for the line parallel to vector $v=\langle a,b,c\rangle$ and passing through the point $\left(x_1,y_1,z_1\right)$ are given by,

  $x=x_1+at$ , $y=y_1+bt$ and $z=z_1+ct$

Calculation:

The component form of the direction vector is $v=\langle 4,0,3\rangle$ . So, the direction numbers are $a=4$ , $b=0$ and $c=3$ . The point is $\left(5,0,10\right)$ .

Substitute 5 for $x_1$ and 4 for $a$ in the equation $x=x_1+at$ .

  $x=5+4t$

Substitute 0 for $y_1$ and 0 for $b$ in the equation $y=y_1+bt$ .

  $y=0$

Substitute 10 for $z_1$ and $3$ for $c$ in the equation $z=z_1+ct$ .

  $z=10+3t$

Therefore, the parametric equations are $x=5+4t$ , $y=0$ and $z=10+3t$ .

(b)

To determine

To find:The set of symmetric equations for the line through the point $\left(5,0,10\right)$ and parallel to the specified vector $v=4i+3k$ .

Answer to Problem 8E

Theset of symmetric equation of line is not possible.

Explanation of Solution

Given information:

The point is $\left(5,0,10\right)$ and vector is $v=4i+3k$ .

Calculation:

It can be observed that the direction numbers are not all non-zero so, the symmetric equation of line is not possible.

Therefore, the set of symmetric equation of line is not possible.