Ask your own question, for FREE!
Mathematics 30 Online
OpenStudy (anonymous):

Suppose vector u=-i+2j+2k, vector v=-2i+j-3k and vector w=-5i+5j-4k. Compute the following values: Abs(vector u)+ abs(vector v) Abs(vector -3u)+ 3abs(vector v)

OpenStudy (zzr0ck3r):

do you know how to find the norm of a vector in \(\mathbb{R}^3\)?

OpenStudy (zzr0ck3r):

\(||\mathbf{x}||:=\sqrt{x_1^2+x_2^2+x_3^2}\)

OpenStudy (zzr0ck3r):

So norm of \(u\) is \(\sqrt{(-1)^2+2^2+2^2}=3\)

OpenStudy (zzr0ck3r):

what is norm of \(w\) ?

OpenStudy (anonymous):

sqrt(66) right?

OpenStudy (zzr0ck3r):

correct

OpenStudy (zzr0ck3r):

nope, your answer will be a real number.

OpenStudy (zzr0ck3r):

by definition norms are real numbers

OpenStudy (zzr0ck3r):

and notice it says "compute the following VALUES"

OpenStudy (zzr0ck3r):

Do you know how to get \(-3u\) ?

OpenStudy (anonymous):

Okay I understand now, thank you so much!

OpenStudy (zzr0ck3r):

np

OpenStudy (anonymous):

-3u is just -3(3) but the abs is 9.

OpenStudy (zzr0ck3r):

\(-3u = 3i-6j-6k \)

OpenStudy (zzr0ck3r):

\(||-3u||=\sqrt{3^2+6^2+6^2}\)

OpenStudy (zzr0ck3r):

when we multiply a vector with a scalar, we multiply each component of the vector by that scalar.

OpenStudy (zzr0ck3r):

so -3u is a vector not a scalar

OpenStudy (zzr0ck3r):

so yes 9:)

OpenStudy (zzr0ck3r):

because \(||-3u||=-3||u||\)

OpenStudy (zzr0ck3r):

err

OpenStudy (zzr0ck3r):

\(||-3u||=|-3|*||u||\)

OpenStudy (zzr0ck3r):

you good?

OpenStudy (anonymous):

okay thanks! what about the abs(4u-3v+w)

OpenStudy (zzr0ck3r):

\(4u-3v+w = 4(-i+2j+2k)-3(-2i+j-3k)+(-5i+5j-4k)=\\-4i+8j+8k+6i-3j+9k-5i+5j-4k=-i+10j+13k\) so we get \(\sqrt{(-1)^2+(10)^2+(13)^2}\)

OpenStudy (anonymous):

So does the abs value have no effect?

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
euphoriiic: I drew more people !! ud83eudd17.
20 minutes ago 41 Replies 4 Medals
euphoriiic: I drew markk ud83eudd17.
4 hours ago 34 Replies 3 Medals
LOLIAteYourMom: u2212243 = u22129(10 + x)
7 hours ago 0 Replies 0 Medals
Bubblezz: Art for @jeromeccv
8 minutes ago 14 Replies 4 Medals
Bubblezz: Art for @jeromecv
11 hours ago 0 Replies 0 Medals
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!