Converting vector-form to cartesian-form line equations in 3D
Convert \frac{x-5}2=y+1=\frac{z+3}6 to vector form
\lambda=\frac{x-5}2 \Rightarrow x=5+2\lambda \lambda=y+1 \Rightarrow y=-1+\lambda \lambda=\frac{z+3}6 \Rightarrow z=-3+6\lambda - Answer:
\vec r = \begin{pmatrix}5\\-1\\-3\end{pmatrix} + \lambda \begin{pmatrix}2\\1\\6\end{pmatrix}
You can see that the first vector corresponds to the negatives of the constant added to each position (e.g.
x-5 becomes5 in the vector), and the second vector corresponds to the denominators of each fraction (e.g.\frac{x-5}2 becomes2 in the vector).
Convert \frac{x+2}4=\frac{y-3}5=z+1 to vector form
\lambda=\frac{x+2}4 \Rightarrow x=-2+4\lambda \lambda=\frac{y-3}5 \Rightarrow y=3+5\lambda \lambda=z+1 \Rightarrow z=-1+\lambda - Answer:
\vec r = \begin{pmatrix}-2\\3\\-1\end{pmatrix} + \lambda \begin{pmatrix}4\\5\\1\end{pmatrix}
flashcards
| Question | Answer |
|---|---|
| What is the first step to convert | Let |
| How do you find the | |
| How do you find the | |
| How do you find the | |
| What is the vector form of the line | |
| In the vector form from the symmetric form, what do the constants in the first vector correspond to? | The negatives of the constant added to each position (e.g. |
| In the vector form from the symmetric form, what does the second vector correspond to? | The denominators of each fraction (e.g. |
| How do you convert | |
| In the conversion of | |
| In the conversion of | |
| In the conversion of |