contestada

Find two unit vectors orthogonal to a=⟨−2,−4,−2âŸİa=⟨−2,−4,−2âŸİ and b=⟨−3,5,2âŸİb=⟨−3,5,2âŸİ Enter your answer so that the first non-zero coordinate of the first vector is positive. First Vector: ⟨⟨ , , âŸİâŸİ Second Vector: ⟨⟨ , , âŸİâŸİ Note: You can earn partial credit on this problem.

Respuesta :

Answer:

u₁= ⟨1/(7*√3),−5/(7*√3) ,−11/(7*√3)âŸİ

u₂= ⟨-1/(7*√3),5/(7*√3) ,11/(7*√3)âŸİ

Step-by-step explanation:

for  a=⟨−2,−4,−2âŸİ and b=⟨−3,5,2âŸİ

a vector orthogonal to a and b can be found through the vectorial product of a and b. Thus

c= a x b[tex]c=\left[\begin{array}{ccc}i&j&k\\-2&-4&-2\\-3&5&2\end{array}\right] = \left[\begin{array}{ccc}-4&-2\\5&2\end{array}\right]*i+\left[\begin{array}{ccc}-2&-2\\-3&2\end{array}\right]*j+\left[\begin{array}{ccc}-2&-4\\-3&5\end{array}\right]*k = 2*i -10*j - 22*k[/tex]

then c₁=⟨2,−10,−22âŸİ and c₂= - c₁= ⟨-2,10,22âŸİ are orthogonal to a and b

the corresponding unit vectors are

u₁=c₁/|c₁| = ⟨2,−10,−22âŸİ / √(2²+(−10)²+(−22)²) = ⟨2,−10,−22âŸİ/(14*√3) =  ⟨1/(7*√3),−5/(7*√3) ,−11/(7*√3)âŸİ

then u₂= - u₁=  ⟨-1/(7*√3),5/(7*√3) ,11/(7*√3)âŸİ

then the unit vectors are

u₁= ⟨1/(7*√3),−5/(7*√3) ,−11/(7*√3)âŸİ

u₂= ⟨-1/(7*√3),5/(7*√3) ,11/(7*√3)âŸİ

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