In the following exercises, vectors u and v are given. Find unit vector w in the direction of the cross product vector u × v . Express your answer using standard unit vectors. 194. Show that u × v and 2 i − 14 j + 2 k cannot be orthogonal for any a real number, where u = i + 7 j − k and v = α i + 5 j + k .
In the following exercises, vectors u and v are given. Find unit vector w in the direction of the cross product vector u × v . Express your answer using standard unit vectors. 194. Show that u × v and 2 i − 14 j + 2 k cannot be orthogonal for any a real number, where u = i + 7 j − k and v = α i + 5 j + k .
In the following exercises, vectors
u
and
v
are given. Find unit vector
w
in the direction of the cross product vector
u
×
v
. Express your answer using standard unit vectors.
194. Show that
u
×
v
and
2
i
−
14
j
+
2
k
cannot be orthogonal for any a real number, where
u
=
i
+
7
j
−
k
and
v
=
α
i
+
5
j
+
k
.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Q2: Using the Laplace transform, find the solution for the following equation
y"" +y" = 6et + 6t + 6. Suppose zero initial conditions (y"" (0) = y"(0) = y'(0) = y(0) = 0).
1- Let A = {A1, A2, ...), in which A, A, = 0, when i j.
a) Is A a π-system? If not, which element(s) should be added to A to become a π-system?
b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and
only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such
class; prove that F is a σ-filed containing A.)
c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you
construct a probability measure on σ(A)? (Hint: use extension theorem.)
2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
3. Let
f(z) =
sin (22) + cos (T2)
2(22+1)(z+1)
Compute f(z)dz over each of the contours/closed curves C1, C2, C3 and C4 shown
below.
Don't use any Al tool
Don't send the same
previous answer that
was Al generated
L
10
-c
x
show ur answer
pe
n and paper then take
Send ur answer in pe
n and paper don't rep
uted ur self down
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.