Line of intersection of planes x - y = 1 and y + z = -3, and L1 is the line of intersection of the planes y - z = 0 and x = -12. a. Determine the point of intersection of L and L1. b. Determine the angle between the lines of intersection. c. Determine the Cartesian equation of the plane that contains the point you found in part a and the two lines of intersection.
Added by Katelyn T.
Step 1
For L, the line of intersection of x - y = 1 and y + z = -3, we can find the parametric equations of the line by setting z = t: x = t + 1 y = -3 - t z = t For L1, the line of intersection of y - z = 0 and x = -12, we can find the parametric equations of the line Show more…
Show all steps
Close
Your feedback will help us improve your experience
P Krishnamurthy and 74 other Calculus 1 / AB 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
Let the abscissa of the point of intersection of the lines $\frac{x}{a}+\frac{y}{b}=2$ and $\frac{x}{b}+\frac{y}{a}=2$ be $c$. Then (a) ordinate of the point of intersection of the lines is $\frac{c}{a+b}$ (b) ordinate of the point of intersection of the lines is $\mathrm{c}$. (c) $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P. (d) $\mathrm{a}, \mathrm{c}, \mathrm{b}$ are in $\mathrm{H.P}$.
a . Find the point of intersection of lines L1 and L2 (make sure to prove that these lines really intersect) L1: (x-3)/2 = (y+1)/4 = (z-2)/-1 L2: (x-1)/4 = (y-1)/2 = (z+3)/4 b. Fins the cosine of the angle between these lines.
Tuli H.
(a) Find the point at which the given lines intersect: $$ r = \langle 1, 1, 0 \rangle + t \langle 1, -1, 2 \rangle $$ $$ r = \langle 2, 0, 2 \rangle + s \langle -1, 1, 0 \rangle $$ (b) Find an equation of the plane that contains these lines.
Madhur L.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD