Write parametric equations of the line through the points (6,-4,4) and (-3,0,-5). Pleaseuse the first point as your base-point when writing the equations.x(t)y(t)z(t)

Given that, the points are P=6,-4,4 and Q=-3,0,-5. That is, P→=6i^-4j^+4k^ and Q→=-3i^+0j^-5k^. It…

Answered: Write parametric equations of the line…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Write parametric equations of the line through the points (6,-4,4) and (-3,0,-5). Please
use the first point as your base-point when writing the equations.
x(t)
y(t)
z(t)

Expert Solution

Step 1

Given that, the points are $P = (6, - 4, 4) a n d Q = (- 3, 0, - 5)$ .

That is, $\vec{P} = 6 \hat{i} - 4 \hat{j} + 4 \hat{k}$ and $\vec{Q} = - 3 \hat{i} + 0 \hat{j} - 5 \hat{k}$ .

It is known that, the parametric form of the line is $\vec{r} (t) = \vec{P} + t \vec{D}$ . where D is the directional vector of a line.

Obtain the value of $\vec{D} = \vec{Q} - \vec{P}$ .

$\begin{array}{rcl} \vec{D} & = & (- 3 \hat{i} + 0 \hat{j} - 5 \hat{k}) - (6 \hat{i} - 4 \hat{j} + 4 \hat{k}) \\ = & - 3 \hat{i} - 6 \hat{i} + 0 \hat{j} + 4 \hat{j} - 5 \hat{k} - 4 \hat{k} \\ = & - 9 i + 4 j - 9 k \end{array}$

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