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

Question

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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RI SƠ 3 years 2021-08-03T08:44:31+00:00 1 Answers 10 views 0

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  1. Maris
    0
    2021-08-03T08:46:04+00:00
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    Answer: hello some part of your question is missing

    Let 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 > )

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )