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ત્રિપરિમાણીય ભૂમિતિ

રેખા x = 4z + 3, y = 2 - 3zની દિકકોસાઈન શોધો.

(0, 1, 1), (0, 4, 4) અને (2, 0, 1) સમરેખ છે ? શા માટે ?

અહીં, $straight a with bar on top space equals space open parentheses 0 comma space 1 comma space 1 close parentheses comma space straight b with bar on top space equals space open parentheses 0 comma space 4 comma space 4 close parentheses bold space bold અન ે bold space straight c with bar on top space equals space open parentheses 2 comma space 0 comma space 1 close parentheses$

$therefore space straight c with bar on top space minus space straight a with bar on top space equals space open parentheses 2 comma space 0 comma space 1 close parentheses space minus space open parentheses 0 comma space 1 comma space 1 close parentheses space equals space open parentheses 2 comma space minus 1 comma space 0 close parentheses bold તથ ા bold space straight b with bar on top space minus space straight a with bar on top space equals space open parentheses 0 comma space 4 comma space 4 close parentheses space minus space open parentheses 0 comma space 1 comma space 1 close parentheses space equals space open parentheses 0 comma space 3 comma space 3 close parentheses bold હવ ે bold comma space open parentheses straight c with bar on top space minus space straight a with bar on top close parentheses space cross times space open parentheses straight b with bar on top space cross times space straight a with bar on top close parentheses$

$equals space open parentheses 2 comma space minus 1 comma space 0 close parentheses space cross times space open parentheses 0 comma space 3 comma space 3 close parentheses equals space open parentheses open vertical bar table row cell negative 1 end cell 0 row 3 3 end table close vertical bar comma space minus open vertical bar table row 2 0 row 0 3 end table close vertical bar comma space open vertical bar table row 2 cell negative 1 end cell row 0 3 end table close vertical bar close parentheses equals space open parentheses negative 3 space minus space 0 comma space minus space open parentheses 6 space minus space 0 close parentheses comma space 6 space minus space 0 close parentheses equals space open parentheses negative 3 comma space minus 6 comma space 6 close parentheses not equal to space 0 with bar on top$

આપેલાં બિંદુઓ અસમરેખ છે.

(1, -2, 1)માંથી પસાર થતી અને રેખાઓ $straight x space plus space 3 space equals space 2 straight y space equals space minus 2 straight z space space bold તથ ા bold space space straight x over 2 space equals space fraction numerator straight y space plus space 6 over denominator 2 end fraction space equals space fraction numerator 3 straight z space minus space 9 over denominator 1 end fraction$ બંનેને લંબરેખાનું સદિશ તેમજ કાર્તેઝીય સમીકરણ મેળવો.

(2, -1, 3) માંથી પસાર થતી અને $2 space straight i with hat on top space minus space 3 space straight j with hat on top space plus space 4 space straight k with hat on top$ દિશાવાળી રેખાનું સદિશ તેમજ કાર્તેઝીય સમીકરણ મેળવો.

(2, 3, -9) અને (4, 3, -5)માંથી પસાર થતી રેખાનું સંમિત સ્વરૂપે અને સદિશ સ્વરૂપે સમીકરણ મેળવો.

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ત્રિપરિમાણીય ભૂમિતિ

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