Sometimes we will want to write vectors in terms of a coordinate grid. To show a vector points
horizontally (along the x-axis), place an x after the magnitude of the vector. To show a vector point
vertically (along the y-axis), place a y after the magnitude.
4) Using the notation above,
i. How would you write d1?
ii. How would you write d2?
iii. How would you write dtotal?
d1=(0,5)
d2=(5,5)

Answer:

III) [tex]d_{1}+ d_{2}=d_{t}[/tex]

Explanation:

I) coordinate (0,5) is the head for [tex]d_{1}[/tex] I will put the tail coordinate as (0,0) but it could be any other number in the x just not in the 5  with the the y being any other value.

II) coordinate (5,5) is the head for [tex]d_{2}[/tex] the tail needs to be in the head of [tex]d_{1}[/tex] being (0,5)

III) coordinates for [tex]d_{t}[/tex] is connecting the tail from [tex]d_{1}[/tex] and the head of [tex]d_{2}[/tex] making it (0,0)[tex](tail)[/tex] and (0,5)[tex](head)[/tex] and is written as [tex]d_{1}+ d_{2}=d_{t}[/tex]

(i) using coordinate grid notation to represent d₁, d₁ = 5y

(ii) using coordinate grid notation  to represent d₂, d₂ = 5x + 5y

(ii) The sum of d₁ and d₂ is written as 5x + 10y

In order to show the horizontal direction of a vector, we will place x after the magnitude of the vector.

Also, to show the vertical direction of a vector, we will place a y after the magnitude of the vector.

(i) Using coordinate grid to represent d₁ = (0, 5)

[tex]d_1 = 0(x) + 5(y)\\\\d_1 = 5y[/tex]

(ii) Using coordinate grid to represent d₂ = (5, 5)

[tex]d_2 = 5x + 5y[/tex]

(iii) The total vector is written as;

[tex]d_1 + d_2 = 5y + (5x + 5y)\\\\d_1 + d_2 = 5y + 5x + 5y\\\\d_1 + d_2 = 5x + 10y[/tex]

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