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Find equations for the line L which satisfies all of the following conditions. (a) L passes...

Find equations for the line L which satisfies all of the following conditions.
(a) L passes through the point (5,6,7).

(b) L is perpendicular to the line x = 2−t, y = 3 + 2t, z = 4t.

(c) L is parallel to the plane 3x−y + z = 17.

Solutions

Expert Solution

L is perpendicular to the line x = 2 - t, y = 3 + 2t, z = 4t

direction vector of line

v1=<-1 , 2 ,4>

Plane 3x - y + z = 17

normal vector

n=<3 , -1 , 1>

To find the direction vector of line parallel to plane and prependicular to line

Point (5,6,7)

Equation of line L

milcah answered 2 years ago
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