Find the norm of (v), and a unit vector, (u = (u_1, u_2, u_3)) that is oppositely directed to the vector (v = (-4, -28, 10)). Use the fact that if (v) is any nonzero vector, then (frac{v}{||v||}) is a unit vector. ( ||v|| = ) ( u = (?, ?, ?) ) Find a point-normal form of the equation of the plane passing through (P(-1, 4, -2)) and having (n = (-2, 1, -1)) as a normal. Complete the equation. ( underline{qquad} = 0)
Added by Bethany A.
Close
Step 1
Given vector U = (-4, -28, 10), the norm of vector U is calculated as: ||U|| = sqrt((-4)^2 + (-28)^2 + 10^2) ||U|| = sqrt(16 + 784 + 100) ||U|| = sqrt(900) ||U|| = 30 ** Show more…
Show all steps
Your feedback will help us improve your experience
Anthony Ramos and 55 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
Find the norm of $v$, and a unit vector that is oppositely directed to v. (a) $v=(2,2,2)$ (b) $\mathbf{v}=(1,0,2,1,3)$
Likhit G.
Find the norm of $v$, and a unit vector that is oppositely directed to v. (a) $\mathbf{v}=(1,-1,2)$ (b) $\mathbf{v}=(-2,3,3,-1)$
Euclidean Vector Spaces
Norm, Dot Product, and Distance in $R^{n}$
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