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Homework Help
Calculus and Beyond Homework Help
Find vectors that are perpendicular & parallel
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[QUOTE="Painguy, post: 4503173, member: 352732"] [h2]Homework Statement [/h2] 1)Give a unit vector a) in the same direction as [B]v[/B]=2[B]i[/B] +3[B]j[/B] b)Perpendicular to [B]v[/B] 2) a) Find a vector perpendicular to the plane z=2+3x-y b)Find a vector parallel to the plane [h2]Homework Equations[/h2] [h2]The Attempt at a Solution[/h2] 1) a) Method 1: [B] u[/B]=[B]v[/B]/||[B]v[/B]|| so i get [B]u[/B]=2/√13[B]i[/B] + 3/√13[B]j[/B] Method 2: ||[B]u[/B]||*||[B]v[/B]||cos(θ)=2 arccos(2/√13)=56.31*=θ ||[B]u[/B]||=1 so [B]u[/B]=cos(56.31)[B]i[/B] + sin(56.31)[B]j[/B]=2/√13[B]i[/B] + 3/√13[B]j[/B] Method 3: [B]u[/B].[B]v[/B]=||[B]v[/B]|| (x[B]i[/B] + y[B]j[/B]).(2[B]i[/B] +3[B]j[/B])=√13 2x + 3y=√13 Here i get stuck. How do i do this and is there any other way? b) Method 1: [B]u[/B].[B]v[/B]=||[B]u[/B]||*||[B]v[/B]||cos(θ)=0 1*√13cos(θ)=0 I get stuck here aswell Method 2: I realized that if i take the angle between [B]v[/B] & the x-axis I should get the angle between u and the x-axis so I can take sin and cos of those angles to get the unit vector perpendicular [B]u[/B]=-3/√13[B]i[/B]+2/√13[B]j[/B] The reason I'm doing all these ways is because I'm curious of the most efficient and proper way to solve the problem. My class is currently covering dot products and I was expecting it all to be as simple as u.v=(x[B]i[/B] + y[B]j[/B]).(2[B]i[/B] +3[B]j[/B])=√13 or (x[B]i[/B] + y[B]j[/B]).(2[B]i[/B] +3[B]j[/B])=0 then I would solve algebraically, but I can't seem to figure out how to do it that way. 2) a) I know that the normal vector is orthogonal to the pane so [B]n[/B]=-3[B]i[/B]+[B]j[/B]+[B]k[/B] is there another way to do this? b) n.v=||[B]n[/B]||*||[B]v[/B]||cos(θ)=0 (-3[B]i[/B]+[B]j[/B]+[B]k[/B]).(x[B]i[/B]+y[B]j[/B] +z[B]k[/B])=0 (-3x +y +z)=0 I get the equation of a similar plane but not the one they originally gave me. Thanks for your help in advance. [/QUOTE]
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Find vectors that are perpendicular & parallel
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