243133continued

243133continued - A par = -16/21i+32/21j+8/21k===a par=8/21...

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r Perp to z =2x+3y +3y-z=0 ……n = 2i+3j-k r par to plane====(pick 2 points) ,0,0) ----Z = 0 and Y=1 then Plug in 3 *1-z=0……Z=5 1,1,5) PQ = (1-0)i+(1-0)j+(5-0)k 5k…take this and multiple by n or (2i+3j-k) 5 ===0, therefore PQ is perp to n Write a=3i+2j-6k as sum of two vectors, one par,one perp To d = 2i-4j+k So a = a par+a perp……A par = (a*d/(//d//))*(d/(//d//), which =u U = 2/SQRT(21)*i – 4/SQRT(21)j + 1/(SQRT(21)) k A par = a*u which = (6/Sq(21)-8/sq(21)-6/Sq(21))* (U)
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Unformatted text preview: A par = -16/21i+32/21j+8/21k===a par=8/21 d A perp = a-a par==(3i+2j-6k)-(a par) A perp=79/21*i+10/21*j-118/21*k Then A = Apar + Aperp Find Normal Vector. Z-5(x-2)=3(5-y) z-5x+10=15-3y-5x+3y+z=5 So n==-5i+3j+k Given v = 3i+4j and F = -6i-8j F par to V = -2(3i+4j) F = -2v. .F par=F.=-6i-8j F perp to V = F=Fpar+Fperp So same, Fperp = 0 Calculate W. .W=F*V ====-2v*v ===-2*//v//^2-2(3^2+4^2). W = -50...
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