Question

Given the non-intersecting lines a: [ egin{cases} x+y-z = 2 \ x-2y+z = 1 end{cases} ] and b: [ egin{cases} 2x-y-z = 4 \ x+y+z = 1 end{cases} ] (a) Find the plane containing a parallel to b. (b) Find the line through P(1,0,1) that intersects with a and b and give its parametric equation.

Name: given the non intersecting lines a begincases xy z 2 x 2yz 1 endcases and b begincases 2x y z 4 xyz 1 endcases a find the plane containing a parallel to b b find the line through p101 that i 02314
Uploaded: 2022-09-19T08:04:34-08:00
Duration: 5 min 55 s
Channel: Adi S
Description: given the non intersecting lines a begincases xy z 2 x 2yz 1 endcases and b begincases 2x y z 4 xyz 1 endcases a find the plane containing a parallel to b b find the line through p101 that i 02314

          Given the non-intersecting lines a:
[
egin{cases}
x+y-z = 2 \
x-2y+z = 1
end{cases}
]
and b:
[
egin{cases}
2x-y-z = 4 \
x+y+z = 1
end{cases}
]

(a) Find the plane containing a parallel to b.
(b) Find the line through P(1,0,1) that intersects with a and b and give its parametric equation.

Added by Vicente C.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

Instant Answer

Solved by Expert Adi S

09/19/2022

Step 1

To find the direction vector of line a, we can take the coefficients of x, y, and z in one of the equations. Let's use the first equation: Direction vector of line a: \[ \vec{v_a} = \begin{bmatrix} 1 \\ 1 \\ -1 \end{bmatrix} \] Similarly, for line b, using the Show more…

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Given the non-intersecting lines a: [ egin{cases} x+y-z = 2 \ x-2y+z = 1 end{cases} ] and b: [ egin{cases} 2x-y-z = 4 \ x+y+z = 1 end{cases} ] (a) Find the plane containing a parallel to b. (b) Find the line through P(1,0,1) that intersects with a and b and give its parametric equation.