Question
Show that the lines $\mathbf{r}_{1}(t)=\langle- 1,2,2\rangle+ t\langle 4,-2,1\rangle$ and $\mathbf{r}_{2}(t)=$ $\langle 0,1,1\rangle+ t\langle 2,0,1\rangle$ do not intersect.
Step 1
Step 1: First, we set the two line equations equal to each other to find the intersection point: \[-1 + 4t_{1} = 0 + 2t_{2}\] \[2 - 2t_{1} = 1 + 0t_{2}\] \[2 + t_{1} = 1 + t_{2}\] Show more…
Show all steps
Your feedback will help us improve your experience
Linh Vu and 72 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Determine whether the lines $\mathbf{r}_{1}(t)=\langle 0,1,1\rangle+ t\langle 1,1,2\rangle$ and $\mathbf{r}_{2}(s)=\langle 2,0,3\rangle+ s\langle 1,4,4\rangle$ intersect, and if so, find the point of intersection.
VECTOR GEOMETRY
Vectors in Three Dimensions
Show that $\mathbf{I}_{1}(t)=(1,2,3)+t(1,0,-2)$ and $\mathbf{l}_{2}(t)=(2,2,1)+t(-2,0,4)$ parametrize the same line.
The Geometry of Euclidean Space
Vectors in Two- and Three-Dimensional Space
Determine whether the lines $\mathbf{r}_{1}(t)=\langle 2,1,1\rangle+ t\langle- 4,0,1\rangle$ and $\mathbf{r}_{2}(s)=\langle- 4,1,5\rangle+ s\langle 2,1,-2\rangle$ intersect, and if so, find the point of intersection.
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD