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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 41 Page 706

Review vector operations. Begin by substituting the vectors in the given expression.

⟨ - 8, 1 ⟩

Practice makes perfect

Before we begin, let's review vector operations.

Vector Addition	⟨ a,b ⟩ + ⟨ c,d ⟩ = ⟨ a+c,b+d ⟩
Vector Subtraction	⟨ a,b ⟩ - ⟨ c,d ⟩ = ⟨ a-c,b-d ⟩
Vector Multiplication	k ⟨ a,b ⟩ = ⟨ ka,kb ⟩

To simplify the given expression, we will begin by substituting the component form of the given vectors, s = ⟨ 2, -6 ⟩ and t = ⟨ - 10,7 ⟩ into the expression. s+t ⇓ ⟨ 2, - 6 ⟩ + ⟨ -10,7 ⟩ Now we can simplify the expression by adding and subtracting the vectors.

⟨ 2,- 6 ⟩ + ⟨ -10, 7 ⟩

▼

Simplify

⟨ a,b⟩+⟨ c,d⟩=⟨ a+c,b+d⟩

⟨ 2+(- 10),- 6+7 ⟩

a+(- b)=a-b

⟨ 2-10,- 6+7 ⟩

Add and subtract terms

⟨ - 8, 1 ⟩

Subchapter links

1 Geometric Mean p.703

2 The Pythagorean Theorem and Its Converse p.703

3 Special Right Triangles p.704

4 Trigonometry p.704

5 Angles of Elevation and Depression p.705

6 The Law of Sines and Law of Cosines p.705

7 Vectors p.706

8 Dilations p.706