Q. Determine whether the lines l and l2 intersect, are parallel, or are skew. y - 2 z+4 x +6 y +2 z-3 12: 3 3 4 4 d Q. find (u(t) v(1)] and (u(t) x v(t)]. dt dt u(t) = cos(2t)i + sin(2t)j +k and v(t) = cos ti + sin tj + k Q. A particle moves along the path y = 3x2 - x with the horizontal component of the velocity equal to Find the 3 2.
Q. Determine whether the lines l and l2 intersect, are parallel, or are skew. y - 2 z+4 x +6 y +2 z-3 12: 3 3 4 4 d Q. find (u(t) v(1)] and (u(t) x v(t)]. dt dt u(t) = cos(2t)i + sin(2t)j +k and v(t) = cos ti + sin tj + k Q. A particle moves along the path y = 3x2 - x with the horizontal component of the velocity equal to Find the 3 2.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![Q. Determine whether the lines l and l2 intersect, are parallel, or are skew.
у - 2
x +6
12:
z+4
y + 2
z- 3
3
3
4
2
d
Q. find [u(t) • v(t)] and (u(t) x v(t)].
u(t) = cos(2t)i + sin(2r)j +k and v(t) = cos ti + sin tj +k
Q. A particle moves along the path y = 3x² - x' with
dt
dt
%3D
%3D
1
the horizontal component of the velocity equal to . Find the
acceleration at the points where the velocity v is horizontal.
Q. find the unit tangent vector T, the principal unit normal vector N, and the binormal
vector B to each vector function. r(t) = 2 sin ti + 2 cos tj+3rk
N(t) =
T'(t)
||T'()|'
and B(t) = T(t) x N(t)
Q. The speed v of sound in a gas depends on the
pressure p and density d of the gas and is modeled by the
formula v(p, d) = k.
where k is some constant. Find the
rate of change of speed with respect top and with respect to d.
Q. If z = f(x, y), where x = u cos 0 – v sin e and
y = u sin 0 + v cos 0, with 0 a constant, show that
af
af
fe,
du
ax
ay
Q. (a) Find an equation of the tangent plane to each surface at the given point.
(b) Find symmetric equations of the normal line to each surface at the given point.
z = In(x? + y?) at (1, –1, In 2)
Q. Find the absolute maximum and the absolute minimum
of the function f(x, y) = 2x? + y? subject to the
constraint x? + y? < 4.
Q. for each vector field F and curve C: r = r(t), find SF•dr.
F(x, y, z) = yi + x²yj + xzk
C is the curve r(t) = e2'i+ e'j+ tk, 0 <t < 1.
Q. find each iterated integral. Identify and graph the region R associated with each integral.
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Transcribed Image Text:Q. Determine whether the lines l and l2 intersect, are parallel, or are skew.
у - 2
x +6
12:
z+4
y + 2
z- 3
3
3
4
2
d
Q. find [u(t) • v(t)] and (u(t) x v(t)].
u(t) = cos(2t)i + sin(2r)j +k and v(t) = cos ti + sin tj +k
Q. A particle moves along the path y = 3x² - x' with
dt
dt
%3D
%3D
1
the horizontal component of the velocity equal to . Find the
acceleration at the points where the velocity v is horizontal.
Q. find the unit tangent vector T, the principal unit normal vector N, and the binormal
vector B to each vector function. r(t) = 2 sin ti + 2 cos tj+3rk
N(t) =
T'(t)
||T'()|'
and B(t) = T(t) x N(t)
Q. The speed v of sound in a gas depends on the
pressure p and density d of the gas and is modeled by the
formula v(p, d) = k.
where k is some constant. Find the
rate of change of speed with respect top and with respect to d.
Q. If z = f(x, y), where x = u cos 0 – v sin e and
y = u sin 0 + v cos 0, with 0 a constant, show that
af
af
fe,
du
ax
ay
Q. (a) Find an equation of the tangent plane to each surface at the given point.
(b) Find symmetric equations of the normal line to each surface at the given point.
z = In(x? + y?) at (1, –1, In 2)
Q. Find the absolute maximum and the absolute minimum
of the function f(x, y) = 2x? + y? subject to the
constraint x? + y? < 4.
Q. for each vector field F and curve C: r = r(t), find SF•dr.
F(x, y, z) = yi + x²yj + xzk
C is the curve r(t) = e2'i+ e'j+ tk, 0 <t < 1.
Q. find each iterated integral. Identify and graph the region R associated with each integral.
xy dy dx
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