1. Find sets of parametric equations and symmetric equations of the line through

ID: 2852482 • Letter: 1

Question

1. Find sets of parametric equations and symmetric equations of the line through the two points (if possible).

(6, ?5, ?2), (-2/5,2/5,1)

(a) Parametric equations

2. Find a set of parametric equations of the line. (Enter your answers as a comma-separated list.)

The line passes through the point (?6, 2, 8) and is perpendicular to the plane given by ?x + 6y + z = 2.

3. Find an equation of the plane passing through the point perpendicular to the given vector or line.

Really need help understanding the subject. Please show all work.

1)(a) Parametric equations

x(t)=6+(-2/5 -6)t =6+(-32/5)t

y(t)=-5+(2/5 +5)t =-5+(27/5)t

z(t)=-2+ (1+2)t =-2+3t

b)symmetric equations

(x-6)/(-32/5)=(y+5)/(27/5)=(z+2)/3

2)line is perpendicular to the plane given by x + 6y + z = 2.

==> direction vector of line =normal vector of plane

normal vector of plane is <-1,6,1>

so direction vector of line is <-1,6,1>

vector representation of line is (6, 2, 8) +t<-1,6,1> =<-6-t,2+6t,8+t>

parametric equations of the line are

x(t)=-6-t

y(t)=2+6t

z(t)=8+t

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