Exercise 24 Page 688

We use the component form of a vector to describe the vector in terms of its horizontal component x and vertical component y. ⟨ x,y ⟩ In other words, the component form of a vector tells us how many units, either in vertical or horizontal directions, we should move from the initial point to end in the terminal point. To write the component form of a vector with initial point ( x_1, y_1) and terminal point ( x_2, y_2), we need to find the differences between the corresponding coordinates.

⟨ x_2- x_1, y_2- y_1 ⟩ Now let's identify the initial and terminal points of the given vector. Remember, the initial point is written as a dot, while the terminal point is shown as an arrow.

Here R is the initial point and S is the terminal point. We can substitute their coordinates into the component form of a vector and simplify. Let's do it!

RS = ⟨ x_2-x_1,y_2-y_1 ⟩

SubstitutePoints

Substitute ( -5,-6) & ( -3,-1)

RS = ⟨ -3-( -5), -1-( -6) ⟩

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

RS = ⟨ -3+5,-1+6 ⟩

AddTerms

Add terms

RS = ⟨ 2,5 ⟩

We found that the component form of the given vector is ⟨ 2, 5⟩. This means that this vector moves a point 2 units right and 5 units up.