Question

1) Consider two vectors A=[20, 4, -6] and B=[8, -2, 6].

a) compute their dot product A.B

b) Compute the angle between the two vectors.

c)Find length and sign of component of A over B (mean Comp A over B)and draw its diagram.

d) Compute Vector projection of B over A (means Proj B over A) and draw corresponding diagram.

e) Compute Orthogonal projection of A onto B.

Answer #1

Consider the following.
u =
−6, −4, −7
, v =
3, 5, 2
(a) Find the projection of u onto
v.
(b) Find the vector component of u orthogonal to
v.

1. Given an ellipsoid with equation
(x−5)^2 /16 +(y−10)^2/ 9+(z−6)^2/ 16= 1 and the plane with equation
y = 19 ﬁnd an equation for the curve of intersection of the two
given surfaces
2.Given vectors a and b, express the vector projection of b onto
a, indicated by p=PROJaB. Now use the decomposition b = projab +
orthab to solve for orthab, which is the vector component of b
which is orthogonal to a.

Consider the two vectors, A and B, for which the length and
angle are given below. What would be the x and y components of the
the vector sum C = A + B? length of A = 3.606, angle A makes with
respect to x-axis = 236.31 degrees length of B = 4.243, angle C
makes with respect to x-axis = 45.000 degrees
Cx=
Cy=

We have two vectors A = (2, 4) and B = (-2, 1). The components
are given with respect to a coordinate system x-y. We chose now
another system of axis x΄- y΄ which is rotated at an angle φ = -300
with respect to x-y. Find out: a) The components of the two vectors
in the new system b) The scalar product of the two vectors in both
systems

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

1. Consider the data 2, 4, 6, 8, 10, 12 and 14. Store them in
?1, and then
(a) Take samples of size 2 with replacement from this
population, list all your samples in the table below:
2,2
2,4
2,6
2,8
4,2
4,4
4,6
6,2
8,2
10,2
(b) Now find the mean of each sample, and place all the sample
means in the table below:
2
3
4
5
6
7
3
4
4
(c) Complete the following probability distribution...

Consider the following data set consisting of two
variables:
x 0 3 5 6 8
y 10 9 7 4 1
(a) Draw a scatter diagram of the data.
(b) Compute the correlation coecient r.
(c) Is there a linear relation between x and y that you are condent
about? If so, in what direction? Justify your answer.

TABLE 3
YEAR
1
2
3
4
5
6
7
8
9
10
NO.OF(‘000)
20
25
28
32
40
45
48
52
56
60
(i). Compute the Trend Projection equation expressing the number
of credit card transactions as a function of time.
(ii) Use that equation to predict the number of credit card
transactions in each of the next two years.

Consider the following time series data.
Month
1
2
3
4
5
6
7
Value
20
28
24
29
25
24
29
(a)
Compute MSE using the most recent value as the forecast for the
next period. What is the forecast for month 8?
(b)
Compute MSE using the average of all the data available as the
forecast for the next period. What is the forecast for month 8?
(c)
Which method appears to provide the better forecast?

Consider the following time series data.
Week
1
2
3
4
5
6
Value
20
12
16
11
18
14
Using the naïve method (most recent value) as the forecast for
the next week, compute the following measures of forecast
accuracy.
(a)
Mean absolute error
If required, round your answer to one decimal place.
(b)
Mean squared error
If required, round your answer to one decimal place.
(c)
Mean absolute percentage error
If required, round your intermediate calculations and final...

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