correcta. Enunciado: Dada la recta que pasa por los puntos \( P(1,3,4) \) y \( Q(3,-2,6) \), ¿cuál es la ecuación paramétrica correspondiente en \( \mathbb{R}^{3} \) ? Seleccione una: \( \begin{aligned} \vec{r}(t) & =(1-2 t, 3-5 t,-4+10 t) \\ \vec{r}(t) & =(1+2 t, 3-5 t,-4+10 t) \\ \vec{r}(t) & =(1-52 t, 3-5 t, 5+11 t) \\ \vec{r}(t) & =(-1+2 t, 3+5 t,-4+10 t)\end{aligned} \)

Determine the standard equation of the ellipse using the stated information. Vertices of the major axis at \( (-1,9) \) and \( (-1,-11) \); length of the minor axis is 10 units. The standard equation of the ellipse is (Simplify your answer. Use integers or fractions for any numbers in the equation.)

In \( \triangle \mathrm{NOP}, n=54 \) inches, \( o=97 \) inches and \( p=95 \) inches. Find the measure of \( \angle \mathrm{N} \) to the nearest degree.

In \( \triangle \mathrm{EFG}, e=880 \) inches, \( f=140 \) inches and \( g=890 \) inches. Find the measure of \( \angle \mathrm{G} \) to the nearest 10th of a degree.

\( \left. \begin{array} { l } { \frac { ( 1 - h ) ^ { 2 } } { a ^ { 2 } } + \frac { ( y - k ) ^ { 2 } } { b ^ { 2 } } = 1 } \\ { \frac { h ^ { 2 } } { a ^ { 2 } } + \frac { [ ( 3 - \frac { \pi } { 2 } ) - k ] ^ { 2 } } { b ^ { 2 } } = 1 } \\ { \frac { ( - 1 - h ) ^ { 2 } } { a ^ { 2 } } + \frac { ( 1 - k ) ^ { 2 } } { b ^ { 2 } } = 1 } \\ { \frac { ( - 5 - h ) ^ { 2 } } { a ^ { 2 } } + \frac { ( 3 - k ) ^ { 2 } } { b ^ { 2 } } = 1 } \end{array} \right. \)

In \( \triangle \mathrm{TUV}, u=4.8 \mathrm{~cm}, v=4.4 \mathrm{~cm} \) and \( \angle \mathrm{T}=84^{\circ} \). Find the length of \( t \), to the nearest 1oth of a centimeter.