Answer to Question #216242 in Analytic Geometry for Dee

Question #216242
(2.1) Find the components of a unit vector satisfying ~v
1
Expert's answer
2021-07-12T15:54:30-0400
"\\vec v\\cdot\\langle3, -1\\rangle=0"

"3v_1-v_2=0=>v_2=3v_1"

"|\\vec v|=1=>v_1^2+v_2^2=1"

"v_1^2+(3v_1)^2=1"

"v_1=\\pm\\dfrac{\\sqrt{10}}{10}"

"\\vec v=\\langle-\\dfrac{\\sqrt{10}}{10}, -\\dfrac{3\\sqrt{10}}{10}\\rangle"

or


"\\vec v=\\langle\\dfrac{\\sqrt{10}}{10}, \\dfrac{3\\sqrt{10}}{10}\\rangle"



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