O Alfred knows his home is about to be over-runto dig a hole in his field and hide it there.O Draw sketch diagrams to show these vectors21otoev rlti Write, in component form, the vector ABrepresented by the line segments joining thefollowing points.Jeops ste d bns o12n4*no nonub sdi as ini s2 3ononRemember a line segmentis part of a line joining twoparticular points. Draw adiagram to help you.dto sbmingso urb en sm hg dos mot innom3i) A(2,3) to B(4, 1)2lii) A(4, 1) to B(2, 3)(ii) A(-2,–3) to B(4, 1)e341 2(Iv A(-2,3) to B(-4, 1)Figure 12.9ogmo) a uo allas isuov lls son oh slnoih(v- A(3, 2) to B(1, 4)(vil A(-3, -2) to B(-1, –4)hieves. He has a box of money and decidesHe plans to run away but to tell his daughterErhel where the money is so that she can goback later and dig it up. How many pieces ofinformation does Alfred need to give Ethel?6 A triangle is formed by the pointsA(1, 4), B(4, 7) and C(1,7).(i) (a) Find the vectors representing the threemedians of the triangle.PSA median joins one vertex to themidpoint of the opposite side.A Draw diagrams to show these vectors and thenwrite them in magnitude-direction form.Use your calculator tocheck your answers.(b) Find the magnitude of each median.number Give your answers in the form abwhere a and b are constants.When a vector is multidirection renias the saThe point X(2, 6) is the centroid of thetriangle.(ii) Find AX. Give your answer in the form aThe vector 2a in Fi| 3i + 4jisito Srlb 1s hdried no i T0G where a and b are constants.nioj li) Show that X divides each of the threemedians in the ratio 2:1.同) 3i – 4j(2,E) miog srf o nigno arlsFigure 12.12Jad V ao UoY ic+ i Ps O PQ and R are points on a plane. Investigatewhen the vector inwhether these situations are possible and, if so,b what can be said about the position of R.liv)3mimber(v)1 PR:(ii) The direction of PR is the same as theand then write them in component form.1 (10, 45°)li (5, 360°)M (10, 135°)(imi) Both PR =QR and the direction of PR istheto 10sfmoi insirog i nwoldirection of QR.li) (5,210°)liv) (10, 270°)ative o vect16q o 21 UOY Othe same as the direction of QR.ail sda(vi) (5,330°)opposite direc249Chapter 12 Vectors

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Description: O Alfred knows his home is about to be over-runto dig a hole in his field and hide it there.O Draw sketch diagrams to show these vectors21otoev rlti Write, in component form, the vector ABrepresented by the line segments joining thefollowing points.

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O Alfred knows his home is about to be over-run by thieves. He has a box of money and decides to dig a hole in his field and hide it there. He plans to run away but to tell his daughter Ethel where the money is so that she can go back later and dig it up. How many pieces of information does Alfred need to give Ethel?

O Alfred knows his home is about to be over-run by thieves. He has a box of money and decides to dig a hole in his field and hide it there. He plans to run away but to tell his daughter Ethel where the money is so that she can go back later and dig it up. How many pieces of information does Alfred need to give Ethel?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

O Alfred knows his home is about to be over-run
to dig a hole in his field and hide it there.
O Draw sketch diagrams to show these vectors
21otoev rlti Write, in component form, the vector AB
represented by the line segments joining the
following points.
Jeops ste d bns o
12
n
4
*no nonub sdi as ini s
2 3
onon
Remember a line segment
is part of a line joining two
particular points. Draw a
diagram to help you.
dto sbmingso urb en sm h
g dos mot innom
3
i) A(2,3) to B(4, 1)
2
lii) A(4, 1) to B(2, 3)
(ii) A(-2,–3) to B(4, 1)
e
3
4
1 2
(Iv A(-2,3) to B(-4, 1)
Figure 12.9ogmo) a uo allas is
uov lls son oh slnoih
(v- A(3, 2) to B(1, 4)
(vil A(-3, -2) to B(-1, –4)
hieves. He has a box of money and decides
He plans to run away but to tell his daughter
Erhel where the money is so that she can go
back later and dig it up. How many pieces of
information does Alfred need to give Ethel?
6 A triangle is formed by the points
A(1, 4), B(4, 7) and C(1,7).
(i) (a) Find the vectors representing the three
medians of the triangle.
PS
A median joins one vertex to the
midpoint of the opposite side.
A Draw diagrams to show these vectors and then
write them in magnitude-direction form.
Use your calculator to
check your answers.
(b) Find the magnitude of each median.
number Give your answers in the form ab
where a and b are constants.
When a vector is multi
direction renias the sa
The point X(2, 6) is the centroid of the
triangle.
(ii) Find AX. Give your answer in the form a
The vector 2a in Fi
| 3i + 4j
isito Srlb 1s hdried no i T0G where a and b are constants.
nioj li) Show that X divides each of the three
medians in the ratio 2:1.
同
) 3i – 4j
(2,E) miog srf o nigno arls
Figure 12.12
Jad V ao UoY ic+ i Ps O PQ and R are points on a plane. Investigate
when the vector in
whether these situations are possible and, if so,
b what can be said about the position of R.
liv)
3
mimber
(v)
1 PR:
(ii) The direction of PR is the same as the
and then write them in component form.
1 (10, 45°)
li (5, 360°)
M (10, 135°)
(imi) Both PR =QR and the direction of PR is
the
to 10s
fmoi insirog i nwoldirection of QR.
li) (5,210°)
liv) (10, 270°)ative o vect
16q o 21 UOY Othe same as the direction of QR.
ail sda
(vi) (5,330°)
opposite direc
249
Chapter 12 Vectors

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