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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

7. Vectors

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Exercise 28 Page 688

The component form of a vector is ⟨ x_2-x_1,y_2-y_1 ⟩.

⟨ 70,350 ⟩

Practice makes perfect

We are given a vector that models the ascent of a firework shell, and we're asked to write this vector in the component form. This means that we need to describe the vector in terms of its horizontal component x and vertical component y. ⟨ x,y ⟩

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 ⟨ x_2-x_1,y_2-y_1 ⟩. 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.

Now, we can substitute these values into the component form of a vector and simplify. We can name our vector f.

f = ⟨ x_2-x_1,y_2-y_1 ⟩

SubstitutePoints

Substitute ( , ) & ( 70,350)

f = ⟨ 70- ,350- ⟩

Subtract terms

f = ⟨ 70,350 ⟩

Subchapter links

Exercises p.687-690