Consider the line which passes through the point P(4, 5, 4), and
which is parallel to...
Consider the line which passes through the point P(4, 5, 4), and
which is parallel to the line x=1+3t, y=2+6t, z=3+1t
Find the point of intersection of this new line with each of the
coordinate planes:
xy-plane: ( , , )
xz-plane: ( , , )
yz-plane: ( , , )
a) Let L be the line through (2,-1,1) and (3,2,2). Parameterize
L. Find the point Q...
a) Let L be the line through (2,-1,1) and (3,2,2). Parameterize
L. Find the point Q where L intersects the xy-plane.
b) Find the angle that the line through (0,-1,1) and (√3,1,4)
makes with a normal vector to the xy-plane.
c) Find the distance from the point (3,1,-2) to the plane
x-2y+z=4.
d) Find a Cartesian equation for the plane containing (1,1,2),
(2,1,1) and (1,2,1)
. Find the line in ? 3 passing (1) through the origin and
parallel to (1,1,-1)...
. Find the line in ? 3 passing (1) through the origin and
parallel to (1,1,-1) (2) though P(3,-1,2) and parallel to Q
(1,1,-1). Hint for (2) : The direction is ??⃗⃗⃗⃗⃗ . You can pick P
or Q as the point it passes through.
Find an equation for the plane that
(a) is perpendicular to v=(1,1,1)v=(1,1,1) and passes through
(1,0,0).(1,0,0)....
Find an equation for the plane that
(a) is perpendicular to v=(1,1,1)v=(1,1,1) and passes through
(1,0,0).(1,0,0).
(b) is perpendicular to v=(1,2,3)v=(1,2,3) and passes through
(1,1,1).(1,1,1).
(c) is perpendicular to the line
l(t)=(5,0,2)t+(3,−1,1)l(t)=(5,0,2)t+(3,−1,1) and passes through
(5,−1,0).(5,−1,0).
(d) is perpendicular to the line
l(t)=(−1,−2,3)t+(0,7,1)l(t)=(−1,−2,3)t+(0,7,1) and passes through
(2,4,−1).