A) Write the line through p=(2,3,−2) in the direction of v¯=<−5,−4,−3> in vector parametric form:
B) Find the parametric and symmetric equations for the line passing through the points P1=(2,2,3) and P2=(1,3,−1) .
PARAMETRIC: x(t)=
y(t)=
z(t)=
SYMMETRIC:
(quotient involving x ) =
(quotient involving y) =
(quotient involving z ) =
C) Find the parametric and symmetric equations for the line passing through the point (1,0,−4) and parallel to the linex=−2+3t, y=4+t, z=2+2t.
PARAMETRIC: x(t)=
y(t)=
z(t)=
SYMMETRIC:
(quotient involving x ) =
(quotient involving y) =
(quotient involving z ) =
D) Consider the two lines
L1:x=−2t,y=1+2t,z=3t and
L2:x=−8+4s,y=4+1s,z=1+5s
Find the point of intersection of the two lines.
E) Find the intersection of the lines r(t)=<−1−2t,17+6t,17+8t> and R(s)=<−10+7s,12−5s,s−5>. Write your answer as a point (a,b,c) where a, b, and c are numbers.