Bu'aan kutaa 12ffaa ba'eera; bu'aa kee eessatti akka ilaaltu

Yaadannoo boqonnaa fi gaaffii shaakalaa

Boqonnaa 8 Herrega kutaa 9: Veektaroota Dayimeenshinii Lamaa

Wanti fuula kana irra jiru hundi boqonnaa 8 kitaaba Herrega kutaa 9 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.

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4
Kaardii
10
Gaaffii shaakalaa boqonnaa 8
247–278
Fuula kitaabaa boqonnaa 8

Boqonnaan 8 maal haguuga

  1. 1.Scalar and Vector Quantities
  2. 2.Representation of a Vector
  3. 3.Vectors Operations
  4. 4.Position Vector
  5. 5.Applications of Vectors in Two Dimensions

Yaadannoo gabaabaa boqonnaa 8

Kaardiiwwan fuula Herrega kutaa 9 irratti boqonnaa kana jala galmaa'an. Tokko tokkoon bani.

Yoom akka itti fayyadamtu

Vektaroota waltParallel hin taane walitti makuun bu'aa isaanii yeroo barbaaddu.

Of eeggadhu

Vektaroonni kallattii tokko yoo qabaatan malee hammoota isaanii akka lakkoofsa salphaatti kallattiin hin ida'inaa.

Grade 9 Mathematics, fuula 247-262 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

∣a∣=x2+y2|\mathbf{a}| = \sqrt{x^2 + y^2}
∣a∣|\mathbf{a}|
hamma vektarii aunits\text{units}
xx
kuttaa dalgee vektarii aunits\text{units}
yy
kuttaa olka'aa vektarii aunits\text{units}

Yoom akka itti fayyadamtu

Dheerina yookiin hamma vektarii fakkii lamaa bifa kolomiitiin kennamee shallaguuf gargaara.

Of eeggadhu

Ida'uun dura kutaalee negaatiivii ta'an gara poozatiiviitti jijjiiruuf iskuweerii gochuu hin dagatin.

Grade 9 Mathematics, fuula 247-262 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

∣PQ⃗∣=(x2−x1)2+(y2−y1)2|\vec{PQ}| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
∣PQ⃗∣|\vec{PQ}|
hamma vektarii PQunits\text{units}
x1x_1
qindeessituu x qabxii jalqabaa Punits\text{units}
y1y_1
qindeessituu y qabxii jalqabaa Punits\text{units}
x2x_2
qindeessituu x qabxii xumuraa Qunits\text{units}
y2y_2
qindeessituu y qabxii xumuraa Qunits\text{units}

Yoom akka itti fayyadamtu

Hamma vektarii qabxii jalqabaa fi xumuraa dirree qindeessituu irratti kenname gidduu jiru shallaguuf itti fayyadamaa.

Of eeggadhu

Kallattii eeguuf qabxii xumuraa irraa qabxii jalqabaa hir'isaa.

Grade 9 Mathematics, fuula 247-262 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

AB⃗+BC⃗=AC⃗\vec{AB} + \vec{BC} = \vec{AC}
AB⃗\vec{AB}
vektarii jalqabaa qabxii A irraa gara qabxii Bunits\text{units}
BC⃗\vec{BC}
vektarii lammaffaa qabxii B irraa gara qabxii Cunits\text{units}
AC⃗\vec{AC}
vektarii bu'aa qabxii jalqabaa A qabxii xumuraa C waliin walqunnamsiisuunits\text{units}

Yoom akka itti fayyadamtu

Qabxiin jalqabaa vektarii lammaffaa qabxii xumuraa vektarii jalqabaa waliin yoo walqunname vektarii bu'aa barbaaduuf itti fayyadamaa.

Of eeggadhu

Qabxii jalqabaa fi xumuraa walqunnamsiisuun dura miilli vektarii lammaffaa mataa vektarii jalqabaa irra ta'uu isaa mirkaneeffadhaa.

Grade 9 Mathematics, fuula 247-262 irraa qophaa'e; osoo hin ba'in dura yeroo lama mirkanaa'e

Gaaffii shaakalaa boqonnaa 8

Gaaffii filannoo 10 boqonnaa kana irratti barreeffaman, tokkoon tokkoon isaanii deebii fi sababa qabu. Deebii banuu dura yaali. Gaaffiin kun Ingiliffaa tiin.

Gaaffii 1

Which of the following describes a scalar quantity?

  1. A.It is fully described by magnitude alone.
  2. B.It is fully described by direction alone.
  3. C.It must have both magnitude and direction.
  4. D.It has direction but no numerical value.
Deebii fi sababa agarsiisi

Deebii: A It is fully described by magnitude alone.

Sababa

A scalar is a quantity that is fully described by a magnitude (or numerical value) alone, without any direction.

Gaaffii 2

Which of the following physical quantities is a vector quantity?

  1. A.Mass of a stone
  2. B.Temperature of a room
  3. C.Velocity of a boat
  4. D.Density of pure water
Deebii fi sababa agarsiisi

Deebii: C Velocity of a boat

Sababa

Velocity requires both a magnitude and a direction, so it is a vector quantity. Mass, temperature, and density are scalar quantities.

Gaaffii 3

When are two vectors said to be equal?

  1. A.When they have the same magnitude and the same direction.
  2. B.When they have the same magnitude but opposite directions.
  3. C.When they have different magnitudes but the same line.
  4. D.When their initial points are at the origin.
Deebii fi sababa agarsiisi

Deebii: A When they have the same magnitude and the same direction.

Sababa

Two vectors are equal if and only if they have the same magnitude and the same direction.

Gaaffii 4

What is the opposite vector of a vector a?

  1. A.A vector with half the magnitude of a in the same direction.
  2. B.A vector with the same magnitude as a, but opposite in direction.
  3. C.A vector with double the magnitude of a in any direction.
  4. D.A vector with zero magnitude.
Deebii fi sababa agarsiisi

Deebii: B A vector with the same magnitude as a, but opposite in direction.

Sababa

The opposite of a vector has the same magnitude as the original vector, but it points in the exact opposite direction. It is denoted by -a.

Gaaffii 5

What is the magnitude of the column vector u = (4, 3)T, where 4 is the horizontal component and 3 is the vertical component?

  1. A.7 units
  2. B.5 units
  3. C.25 units
  4. D.1 unit
Deebii fi sababa agarsiisi

Deebii: B 5 units

Sababa

The magnitude of a column vector (x, y) is |u| = √(x2 + y2). Here, |u| = √(42 + 32) = √(16 + 9) = √25 = 5 units.

Gaaffii 6

Vectors that have the same direction or opposite directions are called:

  1. A.Perpendicular vectors
  2. B.Parallel vectors
  3. C.Equal vectors
  4. D.Unit vectors
Deebii fi sababa agarsiisi

Deebii: B Parallel vectors

Sababa

By definition, vectors that have the same direction or opposite directions are called parallel vectors.

Gaaffii 7

According to the triangle law of vector addition, what is the sum of the directed line segments AB + BC?

  1. A.AC
  2. B.CA
  3. C.BA
  4. D.CB
Deebii fi sababa agarsiisi

Deebii: A AC

Sababa

By the triangle law of vector addition, adding vector AB to vector BC gives the resultant vector AC, connecting initial point A directly to terminal point C.

Gaaffii 8

A vector has an initial point E = (2, 5) and a terminal point F = (2, 10). What is its magnitude |EF|?

  1. A.10
  2. B.7
  3. C.5
  4. D.25
Deebii fi sababa agarsiisi

Deebii: C 5

Sababa

Using the distance formula: |EF| = √((2 - 2)2 + (10 - 5)2) = √(0 + 52) = √25 = 5.

Gaaffii 9

A vector in the first quadrant makes an angle of 37° with the positive horizontal axis (East). If North is along the positive vertical axis, how is its direction correctly written?

  1. A.N 37° E
  2. B.N 53° E
  3. C.E 53° N
  4. D.S 53° E
Deebii fi sababa agarsiisi

Deebii: B N 53° E

Sababa

Vector direction starts from North or South, gives the angle measure, and ends with East or West. The complement of 37° with respect to North is 90° - 37° = 53°. Therefore, the direction is N 53° E.

Gaaffii 10

Vector CD has initial point C = (10, 1) and terminal point D = (5, 5). What is the magnitude |CD|?

  1. A.√41
  2. B.√26
  3. C.9
  4. D.√29
Deebii fi sababa agarsiisi

Deebii: A √41

Sababa

Using the distance formula: |CD| = √((5 - 10)2 + (5 - 1)2) = √((-5)2 + 42) = √(25 + 16) = √41.

Appiin boqonnaa kana irratti gaaffii 12 qaba; utuu hojjettuu ni sirreessa. Kan asii jiran 10 jalqabaa ti.

Fuula kitaabaa boqonnaa 8

Boqonnaan 8 Maxxansa Ministeera Barnootaa keessatti fuula 247 hanga fuula 278 ti.

Maxxansa Ministeera Barnootaa, Ingiliffaa, Fuula 337

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Yaadannoo gabaabaa Herrega kutaa 9 hunda

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