A plane contains the points (3,3,4), (1,2,4) and (1,0,-3). a. Find two vectors that lie in the plane and are not multiples of each other. (4 pts.) b. Find a normal vector to the plane. (6 pts.) c. Find the equation of the plane (in the form ax + by + cz = d). (5 pts.) d. Compute the area of the triangle formed by the three points, using a vector operation. (3 pts.)
Added by Cindy W.
Close
Step 1
Let's call the points A(3,3,4), B(1,2,4), and C(1,0,-3). Vector AB = B - A = (1-3, 2-3, 4-4) = (-2, -1, 0) Vector AC = C - A = (1-3, 0-3, -3-4) = (-2, -3, -7) So, the two vectors are AB = (-2, -1, 0) and AC = (-2, -3, -7). b. Show more…
Show all steps
Your feedback will help us improve your experience
Sam Stansfield and 68 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
The vertices of a triangle PQR have coordinates P(2,-2,4), Q(3,1,-1) and R(3,4,2) on the same plane ̀̑. Find a) the vectors PQ and PR b) a normal vector to the plane ̀̑ c) the area of the triangle PQR d) the Cartesian equation of the plane ̀̑
Craig W.
For the following exercises, the equation of a plane is given. a. Find normal vector $\mathbf{n}$ to the plane. Express $\mathbf{n}$ using standard unit vectors. b. Find the intersections of the plane with the axes of coordinates. c. Sketch the plane. $3 x+4 y-12=0$
Vectors in Space
Equations of Lines and Planes in Space
For the following exercises, the equation of a plane is given. a. Find normal vector $\mathbf{n}$ to the plane. Express $\mathbf{n}$ using standard unit vectors. b. Find the intersections of the plane with the axes of coordinates. c. Sketch the plane. $3 x-2 y+4 z=0$
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