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## Find a unit vector u u in R 2 R2 such that u u is perpendicular to v . v. How many such vectors are there

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Find a unit vector u u in R 2 R2 such that u u is perpendicular to v . v. How many such vectors are there

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Mathematics
3 years
2021-08-03T08:44:31+00:00
2021-08-03T08:44:31+00:00 1 Answers
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## Answers ( )

Answer: hello some part of your question is missingLet v=〈−2,5〉 in R^2,and let y=〈0,3,−2〉 in R^3.

Find a unit vector u in R^2 such that u is perpendicular to v. How many such vectors are there?

answer:One(1) unit vector (

< 5/√29, 2 /√29 > ) perpendicular to〈−2,5〉Step-by-step explanation:let

u = < x , y > ∈/R^2 be perpendicular to v = < -2, 5 > —— ( 1 )

hence :

-2x + 5y = 0

-2x = -5y

x = 5/2 y

back to equation 1

u = < 5/2y, y >

∴ || u || = y/2 √29

∧

u = < 5 /2 y * 2 / y√29 , y*2 / y√29 >

=

< 5/√29, 2 /√29 > ( unit vector perpendicular to < -2, 5 > )