(a) find parametric equations for the line through (1, 3, 8) that is perpendicular to the plane x − y + 4z = 3. (use the parameter t.) (x(t), y(t), z(t))
(b) in what points does this line intersect the coordinate planes?

a)    x = 1 + t

      y = 3 -  t

      z = 8 +2t

b)  In XY plane (-3,-1,0)

    In YZ  plane (0, 4,  6)

    In XZ plane ( 4,0,14)

Step-by-step explanation:

The equation of plane is given as

x -y +2z = 5

a)

COMPARE THE ABOVE EQUATION with Ax+ By +Cz = d

A = 1, B = -1. C =  2

N = (1,3,8) {GIVEN POINT]

the parametric eqn. of line P(Xo , Yo, Zo) and prependicular plan Ax+ By+ Cz = d is given as

X = Xo+ At

Y = Yo + Bt

Z=Zo + Ct

x = 1 + t

y = 3 -  t

z = 8 +2t

b) Line intersecting XY plane if z equal to zero i.e

0 = 8 +  2t

t =-4

for t = -4

x = -3, y = -1, z = 0

In YZ plane, x = 0

t = -1

interesting point will be

(0, 4,  6)

In XZ plane, Y =  0

t = 3

interesting point will be

(4, 0,  14)

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