Algebra Archive: Questions from May 15, 2023
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Current Attempt in Progress \[ \begin{array}{l} \text { Compute }\left(T_{3} \circ T_{2} \circ T_{1}\right)(x, y) . T_{1}(x, y)=(-5 y, 7 x, x-5 y) \text {, } \\ T_{2}(x, y, z)=(y, z, x), T_{3}(x, y, z
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given the vectors \( \vec{u}=(1,2,3), \vec{v}=(2,0,1) \quad \vec{w}=(-1,3,0) \), find: \[ \begin{array}{l} \vec{u} \cdot \vec{v}, \vec{v} \cdot \vec{w}, \vec{u} \cdot \vec{w}, \vec{v} \cdot \vec{u} \\
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Consider the plane π:6x−3y+2z=0 and the point Q=(13,−2,7).
If the point P=(α,β,γ) is the point in the π plane closest to Q,
then we can ensure that the value of α+β+γ is:
Considere el plano \( \pi: 6 x-3 y+2 z=0 \) y el punto \( Q=(13,-2,7) \). Si el punto \( P=(\alpha, \beta, \gamma) \) es el punto en el plano \( \pi \) más cercano a \( Q \), podemos asegurar entonce
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Given the line: L:(x,y,z)=(1,3,3)+t(4,1,−6) And the
plane whose Cartesian equation is:
3x−y+2z=−3
If (α,β,γ) represents the point of intersection
between them, determine the value of β.
Dada la recta: \[ L:(x, y, z)=(1,3,3)+t(4,1,-6) \] Y el plano cuya ecuación cartesiana es: \[ 3 x-y+2 z=-3 \] Si \( (\alpha, \beta, \gamma) \) representa el punto de intersección entre ambos, determ
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