Question

What is the length of the projection of the unit vector of the
direction unit vector of the line x = 1 + 2t, y = 3-t, z = 5 + 2t
overthe vector of the plane 2x + 3y-6z + 8 = 0? If your answer is a
fraction write it in the abcd / efgh style (no spaces between what
you write)

Answer #1

(a) Find the distance between the skew lines l1 and l2 given
with the vector equations l1 : r1(t) = (1+t)i+ (1+6t)j+ (2t)k; l2 :
r2(s) = (1+2s)i+ (5+15s)j+ (−2+6s)k.
(b) Determine if the plane given by the Cartesian equation −x +
2z = 0 and the line given by the parametric equations x = 5 + 8t, y
= 2 − t, z = 10 + 4t are orthogonal, parallel, or neither.

1) Find an equation of the plane. The plane through the point
(7, 0, 4)and perpendicular to the line x = 3t,y = 3 − t,z = 1 +
7t
2) Consider the following planes.x + y + z = 2, x + 6y + 6z =
2
(a) Find parametric equations for the line of intersection of
the planes. (Use the parameter t.) (x(t), y(t), z(t))
=
(b)Find the angle between the planes. (Round your answer to one
decimal...

1.
a) Find a value of x other than 0 such that the vectors <-3x,
2x> and <4, x> are perpendicular
b) find the domain of the vector function r (t) = <sin (t),
ln (t), 1 / (t-1)>
c) Determine if the sequence converges or diverges, if it
converges determines its limit
ln (2 + e ^ n) / 2020n
d) Find the point (a, b, c) where the line x = 1-t, y = t, z = 1...

please answer all of them; only need final answer
h. The length of the vector c = (2, -3, 1) is?
i. If |r| = 4, then the value of |-5r| is?
j. The cross product of vectors a = (-1, 4, 6) and b = (3, 0, 2)
is?
k. The vectors v = (3, 4) is projected onto the x-axis The
length of the projection is?
l. Rounded to the nearest integer, a two-dimensional vector with
length 13...

For the following equation x=2t^2,y=3t^2,z=4t^2;1 less
or equal to t less or equal to 3
i) Write the positive vector tangent of the curve with parametric
equations above.
ii) Find the length function s(t) for the curve.
iii) Write the position vector of s and verify by differentiation
that this position vector in terms of s is a unit tangent to the
curve.

Consider plane P: 4x -y + 2z = 8, line: <x, y, z> =
<1+t, -1+2t, 3t>, and point Q(2,-1,3)
b) Find the perpendicular distance between point Q and plane
P

1)Find sets of parametric equations and symmetric equations of
the line that passes through the two points. (For the line, write
the direction numbers as integers.)
(5, 0, 2), (7, 10, 6)
Find sets of parametric equations.
2) Find a set of parametric equations of the line with the given
characteristics. (Enter your answer as a comma-separated list of
equations in terms of x, y, z, and
t.)
The line passes through the point (2, 1, 4) and is parallel to...

An object moves in a coordinate system with
velocity vector v(t) = < sqrt(1+2t), tcos(?t), tsin(?t) > for
t >= 0.
?=pi
a. Find the equation of the tangent line to
the objects path when it reached the
origin.
b. When the object reached the origin, with
what angle did it strike the xy-plane?
c. Give the (unit) tangent, (unit) normal, and
binormal directions for the object when it hits the
xy-plane.
d. Give a vector-valued function describing
the objects...

Two long, parallel conductors, separated by 13.0 cm,
carry currents in the same direction. The first wire carries a
current I1 = 3.00 A, and the second carries
I2 = 8.00 A. (See figure below. Assume the
conductors lie in the plane of the page.)
(a) What is the magnetic field created by
I1 at the location of I2?
magnitude Tdirection ---Select--- in the +x direction in the -x
direction in the +y direction in the -y direction in the...

1. Consider the plane 4x+y-2z=4 and
the line r(t) = < t, -2t,
-tt >.
a. find the unit normal vector N of the plane.
b. as a function of t find the distance between
r(t) and the plane.
2. Consider a fruit fly flying a room with velocity
v(t) = < -sin(t), cos(t), 1 >
a. if the z = 1 + 2(pi) is the room's ceiling, where
will the fly hit the ceiling?
b. if the temperature in...

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