SLC S23 Week5 || Coordinates&Vectors

Hi :

Hi everyone I am fine and I hope that you all will also be fine and will be doing g great work at Steemit.I am M.Abdullah and today I am participating in a contestCoordinates&Vectorswhich is organized by @sergeyk .So I will do all the homework and will participate in this 5th week of mathematics. So let us start our homework.

Canva

---

---

TASK : 1

NUMBER LINE :

The number line is generally a straight and vertical line where the number s are placed in an order like the whole number order like 0,1, 2, 3 ... and the zero s called the origin and also the middle point from where the numbers on the right are ever while the numbers on the left are negative .

Coordinate Plane:

so the coordinate plan is made up of two lines that are perpendicular. The first line is known as the Y-axis and the other is known as the X-axis. These lines intersect each other at point O, O is called the origin.

First Learning Of Coordinate Plane:

I first started learning the coordinate system in maybe 6 and 7 grade which seemed a little bit difficult at the start but after much practice it became a pice of cake for me. and the coordinate system is very easy as there is only to deal will the Y axis and X axis.But now it is difficult because the use of coordinate system in decimal number is littleb it hard.

---

---

TASK : 2

So for task number 2 the given points are ;

• A (-3,11)
• B (4,7)
• C (0,4)
• D (4,0)
• E (-4,-7)
• F(11,3)
  So to join the pairs you have to use the subtraction method which is like this ;

For Vector AB :

AB = (4-(-3),(7-11))
AB = ( 4 + 3),(-4)
AB = (7,-4)

For Vector AC :

AC = (0 -(-3),4-11)
AC = (0+3),-7)
AC = (3,-7)

For Vector AD :

AD = (4-(-3),0-11)
AD = (4+3,-11)
AD = (7,-11)

For Vector AE :

AE = (-4 - (-3),-7-11)
AE = (-4+3,-18)
AE = (-1.-18)

For Vector AF :

AF = (11-(- 3),3-11)
AF = (11+3,-8)
AF = (14,-8)

---

---

TASK : 3

You can see in the below picture that I have put all the coordinates A,B and C in the coordinate system
as you can know from the coordinate system in A(3,7) starts from the origin point O and goes 3 Units right means that it is positive while 7 units go up while in B(-1,-3) it is also starting from the
origin(every point starting point will be O origin ) O and it go 1 unit left and 3 units go downward. and in C(1,5) the starting point will be O origin as usual and its 1 unit will go to the right and 5 unit will go in an upward direction as you can see in the below picture ;

Find A+B+C :

for finding A+B+C we will add the coordinates like this:

A+B+C = (3+ (-1)+1,7+(-3)+5)
A+B+C = (3-1+ 1,7-3+5)
A+B+C = (2+1,4+5)
A+B+C = (3,9)

The answer of A+B+C is (3,9) you can also do it in a coordinate system.

---

---

TASK : 4

So for task number 4 we have to make a vector which would be A = (2,6) and B = (4,8).
For finding AB we will use the subtraction method.

Find AB :

AB = (4-2 ,8-6)
AB = (2,2)

Now to double the vector simply multiply the elements of vector by 2 as ;

Double Of AB :

2.AB = (2.2,2.2)
2.AB = (4,4)

So the double the vector is equal to (4,4) and here in the above multiplication the dot (.) represent multiplication .

---

---

TASK : 5

For task number 5 there is a need of Vectors such that A, B and K So the Vector ;
A = (2,3)
B = (-1,4)
K = (3,-2)

U = A + B:

U = (2+(-1),3+4)
U = (2 - 1,7)
U = (1,7)

V = B-K:

V = (-1-3,4-(-2))
V = (-4,4+2)
V = (-4,6)

U + V:

Now after finding U and V we will find U+V as ;

U+V = (1+(-4),7+6)
U+V = (1-4,13)
U+V = (-3,13)

U - V:

So now after finding U+V now we will find U- V as ;

U - V = (1-(-4),7-6)
U - V = ((1+4),1)
U -V = (5,1)
So it is the answer of the U - v.

U = (1,7)
V = (-4,6)
U+V = (-3,13)
U -V = (5,1)

---

---

BONUS TASK

Vector Projection :

The vector projection is a method by which we can find that the first vector A projection onto the second vector B. Through the projection method, we can find the amount of Vector A point on the Vector B.

Formula :

---

---

Thats All I hope that you all like my post and now I am inviting some of my friend to visit my post .They are ;

• @kouba01
• @abdullahw2
• @bahrol.

Contest Organizer : @sergeyk

---

---