Question

f(k) = f(i) f(j) = (rs)(r^2) = ____

f(-k) = f(j) f(i) = (r^2)(rs) = ____

Are the two the same?

Answer #1

Hi if you have doubts please comment here I will help you

Use the helix: r(t)= (bcost)i +(bsint)j +(ct)k , b>0
I only need e and f. I posted another question where only a-d
were answered if you want to use that work to answer e and f. thank
you
a. find the unit tangent vector
b. find the principal normal vector
c.find the curvature
d.find the binormal vector
e. Find the tangential component of acceleration.
f. find the normal component of acceleration using both
formulas, try to verify that they are...

Are the vectors a = i + j − k, b = i − j + k, and c = i + j + k
coplanar?

Use Stoke’s Theorem to evaluate Z C F~ · d~r where F~ = 2y~i+
6z~j + 5x~k and C is the triangle with vertices (corners) at (5, 0,
0), (0, 5, 0), and (0, 0, 5) oriented clockwise when viewed from
above

(1 point) If C is the curve given by
r(t)=(1+5sint)i+(1+2sin2t)j+(1+3sin3t)k, 0≤t≤π2 and F is the radial
vector field F(x,y,z)=xi+yj+zk, compute the work done by F on a
particle moving along C.

Find the curvature of ~r(t) = (t3 −5)~ i + (t4 + 2)~ j + (2t +
3)~ k at the point P(−6,3,1)?

Force F= (2.84 i - 1.39 k)N acts on a pebble with position
vector r= (6.54 j - 1.60 k)m , relative to the origin. What is the
resulting torque acting on the pebble about (a)
the origin and (b) a point with coordinates (4.96
m, 0, -1.43 m)?

CountingSort(A, B, k)
for i=1 to k
C[i]= 0;
for j=1 to n
C[A[j]] += 1;
for i=2 to k
C[i] = C[i] + C[i-1];
for j=n downto 1
B[C[A[j]]] = A[j];
C[A[j]] -= 1;
illustrate the operation of COUNTING-SORT on the array A =
{6,0,2,0, 1, 3, 5, 6, 1, 3, 2}. Specifically, show the four arrays
A, B, C, and C'.

1. Consider
three
vectors:
(
8
marks)
C i j k
B i j k
A i j k
0ˆ 3 ˆ 5 ˆ
2ˆ 7 ˆ 1ˆ
4ˆ 6 ˆ 2 ˆ
= + +
= + −
= + −
!
!
!
1.1 Evaluate
D=
2A+B?
(2
marks)
1.2 Evaluate
2A•(-‐B)
(2
marks)
1.3 Find
the
angle
between
D
and
2C
using
cross
product
method
(4
marks

The Fibonacci series is given by; F0=0, F1=1,F2=1,
F3=2,F4=3,…F(i)=F(i-1)+F(i-2)
Given that r^2=r+1. Show that F(i) ≥ r^{n-2}, where F(i) is the
i th element in the Fibonacci sequence

What is the vector product of A = 4 (i) - 3 (j) - 5 (k) and B =
5 (i) - 4 (j) + 2 (k)?
22
9 (i) - 7 (j) - 3 (k)
14 (i) - 17 (j) - 1 (k)
-26 (i) - 33 (j) - 1 (k)
20 (i) + 12 (j) - 10 (k))

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