Question
Show that the equations $x=3+t, y=2 t, z=1-t$ satisfy the equations $x+y+3 z=6$ and $x-y-z=2$ What does this tell you about the curve parameterized by these equations?
Step 1
Given: \(x = 3 + t\) \(y = 2t\) \(z = 1 - t\) Substitute these into \(x + y + 3z = 6\): \((3 + t) + (2t) + 3(1 - t) = 6\). Show more…
Show all steps
Your feedback will help us improve your experience
William Mead and 56 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
Write the curve described by the equations $x-1=2 y+1=3 z+2$ in parametric form.
Vector-Valued Functions
Divergence and Curl
Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by climinating the parameter. $$x=2 t-3, \quad y=3 t+1$$
Conics, Parametric Equations, and Polar Coordinates
Plane Curves and Parametric Equations
Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. $x=3-2 t, \quad y=2+3 t$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD