1) Find the volume of the parallelopiped with adjacent edges PQ,
PR, PS where P ( -2,-3,-3) , Q (0,0,0) , R (-3,-4,-4) and S (
4,-5,-1)
2) Find the area of the parallelogram with vertices A (2,2) .B (
7,3) C (4,7) and D (9,8)
Find the volume of the parallelepiped with adjacent edges
PQ, PR, PS.
P(3, 0, 2), Q(−1, 2,
7), R(4, 2, −1), S(0,
5, 3)
Cubic units
If a = (2, −1, 5)
and b = (4, 2, 1),
find the following.
a × b =
b × a=
If
a = i − 5k and b = j + k, find a × b
(2) PQRS is a quadrilateral and M is the midpoint of PS.
PQ = a, QR = b and SQ = a – 2b.
(a) Show that PS = 2b.
Answer(a)
[1]
(b) Write down the mathematical name for the quadrilateral PQRM,
giving reasons for your answer.
Answer(b)
..............................................................
because
...............................................................
.............................................................................................................................................................
[2]
__________
A tram leaves a station and accelerates for 2 minutes until it
reaches a speed of 12 metres per second.
It continues at this speed for...
If the pth term of an arithmetic progression is \( \frac{1}{q} \) and the qth term is \( \frac{1}{p} \) , prove that the sum of the first pq terms must be \( \frac{1}{2}(pq+1) \).
Consider the hypothesis test below.
H 0: p 1
- p 2 0
H a: p 1
- p 2 > 0
The following results are for independent samples taken from the
two populations.
Sample 1
Sample 2
n1 = 100
n2 = 300
p1 = 0.24
p2 = 0.13
Use pooled estimator of p.
What is the value of the test statistic (to 2
decimals)?
What is the p-value (to 4
decimals)?
With = .05, what is your hypothesis testing
conclusion?
Let A = 0 2 0
1 0 2
0 1 0 .
(a) Find the eigenvalues of A and bases of the corresponding
eigenspaces.
(b) Which of the eigenspaces is a line through the origin? Write
down two vectors parallel to this line.
(c) Find a plane W ⊂ R 3 such that for any w ∈ W one has Aw ∈ W
, or explain why such a plain does not exist.
(d) Write down explicitly a diagonalizing...
Let A = 0 2 0
1 0 2
0 1 0 .
(a) Find the eigenvalues of A and bases of the corresponding
eigenspaces.
(b) Which of the eigenspaces is a line through the origin? Write
down two vectors parallel to this line.
(c) Find a plane W ⊂ R 3 such that for any w ∈ W one has Aw ∈ W
, or explain why such a plain does not exist.
(d) Write down explicitly a diagonalizing...