1. Determine whether the lines are parallel, perpendicular or
neither. (x-1)/2 = (y+2)/5 = (z-3)/4 and...
1. Determine whether the lines are parallel, perpendicular or
neither. (x-1)/2 = (y+2)/5 = (z-3)/4 and (x-2)/4 = (y-1)/3 =
(z-2)/6
2. A) Find the line intersection of vector planes given by the
equations -2x+3y-z+4=0 and 3x-2y+z=-2
B) Given U = <2, -3, 4> and V= <-1, 3, -2> Find a. U
. V b. U x V
Consider the following planes.
x + y + z = 1, x + 3y + 3z =...
Consider the following planes.
x + y + z = 1, x + 3y + 3z = 1
(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 place.)
°
a= 1, b =6 , c= 4
T(x,y,z) =(x^2 )y +(y^2 )z
Find the directional derivative...
a= 1, b =6 , c= 4
T(x,y,z) =(x^2 )y +(y^2 )z
Find the directional derivative of T at the point (a − 1, a, a +
1) along
the direction of the vector < a, b, c >.
3. Consider the following two lines:
x = c + t, y = 1 + t,...
3. Consider the following two lines:
x = c + t, y = 1 + t, z = 5 + t and x = t, y = 1 - t, z = 3 +
t.
Is there a value c that makes the two lines intersect? If so,
find it. Otherwise, give a reason.
4. A particle starts at the origin and moves along the shortest
path to the line determined by the two points P =(1,2,3) and Q
=(3,-2,-1)....
. Find the intersection of the planes x − y + 5z = 9 and
x...
. Find the intersection of the planes x − y + 5z = 9 and
x = 1 + s − t
y = 1 +2 s − t
z = 2 − s + t .
(a) Find the line ℓ1 perpendicular to the first of these planes
and passing across the point (1, 2, 2).
(b) Find a line ℓ2 perpendicular to the second of these planes
and passing across the point (1, 2, 2).
(c) Find the...
f(x, y, z) =
xe4yz, P(1, 0, 3),
u = <2/3, -1/3, 2/3>
(a) Find the...
f(x, y, z) =
xe4yz, P(1, 0, 3),
u = <2/3, -1/3, 2/3>
(a) Find the gradient of f.
∇f(x, y, z) =
< , , >
(b) Evaluate the gradient at the point P.
∇f(1, 0, 3) = < , ,
>
(c) Find the rate of change of f at P in the
direction of the vector u.
Duf(1, 0, 3) =