Answer to Question #301385 in Analytic Geometry for pianowoman

Question #301385

3a. Consider the line L that passes through the point P0(4, 2, -3) is parallel to the vector


⟶ [ 2

u = -1 <----Matrix

6]


Find a vector equation and the parametric equations of the line L.


b. Find the point of intersection of the line L with the xy-plane (z = 0).



1
Expert's answer
2022-02-23T12:53:44-0500

3.

a.  The vector equation of the line containing P0(4,2,3)P_0(4, 2, -3) and parallel to u=[216]\vec u=\begin{bmatrix} 2\\ -1 \\ 6 \end{bmatrix} is


r=[4+2t2t3+6t]\vec r=\begin{bmatrix} 4+2t\\ 2-t \\ -3+6t \end{bmatrix}

The corresponding parametric equations are


x=4+2t,y=2t,z=3+6tx=4+2t, y=2-t, z=-3+6t

b.

We have the line L


x42=y21=z+36\dfrac{x-4}{2}=\dfrac{y-2}{-1}=\dfrac{z+3}{6}

If z=0z=0


x42=y21=0+36\dfrac{x-4}{2}=\dfrac{y-2}{-1}=\dfrac{0+3}{6}

x=5,y=3/2x=5, y=3/2

Point (5,3/2,0)(5, 3/2, 0) is the point of intersection of the line L with the xy-plane.



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