Question

1. Given the point P(5, 4, −2) and the point Q(−1, 2, 7) and R(0, 3, 0) answer the following questions • What is the distance between P and Q? • Determine the vectors P Q~ and P R~ ? • Find the dot product between P Q~ and P R~ . • What is the angle between P Q~ and P R~ ? • What is the projP R~ (P R~ )? • What is P Q~

Answer #1

Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and let q = (2,
4, 9, 5, 10, 6, 11, 7, 0, 8, 1, 3) be tone rows. Verify that p =
Tk(R(I(q))) for some k, and find this value of k.

If p(x) and q(x) are arbitrary polynomials of degree at most 2,
then the mapping
=p(−1)q(−1)+p(0)q(0)+p(2)q(2) defines an inner product in P3.
Use this inner product to find
, ||p||, ||q||, and the angle θ between p(x) and q(x) for
p(x)=2x^2+3 and q(x)=2x^2−6x.

1.
(1 point)
Find the distance the point P(1, -6, 7), is to the plane through
the three points
Q(-1, -1, 5), R(-5, 2, 6), and S(3, -4, 8).
2.
(1 point) For the curve given by
r(t)=〈−7t,−4t,1+7t2〉r(t)=〈−7t,−4t,1+7t2〉,
Find the derivative
r′(t)=〈r′(t)=〈 , , 〉〉
Find the second derivative
r″(t)=〈r″(t)=〈 , , 〉〉
Find the curvature at t=1t=1
κ(1)=κ(1)=

Find the area of the parallelogram PQRS with vertices P(1, 1,
0), Q(7, 1, 0), R(9, 4, 2), and S(3, 4, 2).

A (–4, –1, 2), B (3, –2, –1) and C (–1, 3, –4),
AB= 7? − ? − 3?
CB = 4? − 5? + 3?
AC = 3? + 5? - 2?
Question 7: Express the vector AC as the sum of two vectors: AC
= ? + ?, where ? is parallel to the vector CB and ? is
perpendicular to CB. Given that AC ∙ CB = −26 and that CB = √50,
determine the y-component of...

Given the following unordered array:
[0]
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
W
X
D
T
P
N
R
Q
K
M
E
If the array was being sorted using
the SHELL sort and the halving
method,
and sorting into ASCENDING
order as demonstrated in the course content,
list the letters in the resulting
array, in order AFTER the FIRST pass.
[0]
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]

P=
1 0 0
0
.2 .3
.1 .4
.1
.2 .3 .4
0
0
0 1
(a) Identify any absorbing state(s).
(b) Rewrite P in the form:
I O
R Q
(c)Find the Fundamental Matrix, F.
(d)Find FR

Suppose g: P → Q and f: Q → R where P = {1, 2, 3, 4},
Q = {a, b, c}, R = {2, 7, 10}, and f and g are defined by
f = {(a, 10), (b, 7), (c, 2)} and g = {(1, b), (2, a), (3, a), (4,
b)}.
(a) Is Function f and g invertible? If yes find f −1
and g −1 or if not why?
(b) Find f o g and g o...

Find the lengths of the sides of the triangle PQR. (a) P(4, −1,
−3), Q(8, 1, 1), R(2, 3, 1)
|PQ| =
|QR| =
|RP| =
(b)
P(5, 1, −1), Q(7, 3,
0), R(7, −3, 3)
|PQ|
=
|QR|
=
|RP|
=

Let P be the point (2, 3, -2). Suppose that the point P0(-3, -2,
7) is 1/4 of the way from P to Q. Find the point Q.

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