Vector Projections and Resolutions

Vector u and its Resolution relative to v

นิพจน์ 11: "u" Subscript, "x" , Baseline equals 5.6 3

negative 10

นิพจน์ 12: "u" Subscript, "y" , Baseline equals 10.5 6

negative 10

10.5 6

`\mathbf{u}` "u" Subscript, "e" "n" "d" , Baseline equals left parenthesis, "u" Subscript, "x" , Baseline , "u" Subscript, "y" , Baseline , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 5.6 3 , 10.5 6 , right parenthesis

นิพจน์ 14: "u" equals vector left parenthesis, left parenthesis, 0 , 0 , right parenthesis , "u" Subscript, "e" "n" "d" , Baseline , right parenthesis

นิพจน์ 15: "u" Subscript, "p" "r" "o" "j" "v" , Baseline equals StartFraction, "u" times "v" Over StartAbsoluteValue, "v" , EndAbsoluteValue squared , EndFraction "v"

`\mathrm{proj}_{\mathbf{v}}(\mathbf{u})` left parenthesis, "u" Subscript, "p" "r" "o" "j" "v" , Baseline .end . "x" , "u" Subscript, "p" "r" "o" "j" "v" , Baseline .end . "y" , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 7.9 0 9 2 3 7 9 9 , 2.1 4 1 3 1 1 6 9 , right parenthesis

นิพจน์ 17: "u" minus "u" Subscript, "p" "r" "o" "j" "v" , Baseline

`\mathrm{proj}_{\mathbf{v^\perp}}(\mathbf{u})` left parenthesis, left parenthesis, "u" minus "u" Subscript, "p" "r" "o" "j" "v" , Baseline , right parenthesis .end . "x" , left parenthesis, "u" minus "u" Subscript, "p" "r" "o" "j" "v" , Baseline , right parenthesis .end . "y" , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, negative 2.2 7 9 2 3 7 9 9 , 8.4 1 8 6 8 8 3 1 , right parenthesis

ซ่อน ป้ายกำกับ segment left parenthesis, "u" .end , left parenthesis, "u" Subscript, "p" "r" "o" "j" "v" , Baseline .end . "x" , "u" Subscript, "p" "r" "o" "j" "v" , Baseline .end . "y" , right parenthesis , right parenthesis

ป้ายกำกับ

ซ่อน ป้ายกำกับ segment left parenthesis, "u" .end , left parenthesis, left parenthesis, "u" minus "u" Subscript, "p" "r" "o" "j" "v" , Baseline , right parenthesis .end . "x" , left parenthesis, "u" minus "u" Subscript, "p" "r" "o" "j" "v" , Baseline , right parenthesis .end . "y" , right parenthesis , right parenthesis

ป้ายกำกับ

ดำเนินการโดย

StartBold Font, "v" EndBold Font

StartBold Font, "v" Superscript, perpendicular , Baseline EndBold Font

StartBold Font, "u" EndBold Font

proj Subscript, StartBold Font, "v" EndBold Font , Baseline ( StartBold Font, "u" EndBold Font )

proj Subscript, StartBold Font, "v" Superscript, perpendicular , Baseline EndBold Font , Baseline ( StartBold Font, "u" EndBold Font )