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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

7. Vectors

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Exercise 43 Page 689

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

⟨ 4, - 4 ⟩

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, f = ⟨ -4, -2 ⟩, g = ⟨ 6,1 ⟩, and h = ⟨ 2, -3 ⟩, into the expression. f+g+h ⇓ ⟨ - 4, - 2 ⟩ +⟨ 6,1 ⟩ + ⟨ 2, -3 ⟩ Now we can simplify the expression by adding the given vectors.

⟨ - 4,- 2 ⟩ +⟨ 6, 1 ⟩ + ⟨ 2, -3 ⟩

▼

Simplify

⟨ a,b⟩+⟨ c,d⟩=⟨ a+c,b+d⟩

⟨ - 4+6,- 2 + 1 ⟩ + ⟨ 2, -3 ⟩

Add terms

⟨ 2,- 1 ⟩ + ⟨ 2, -3 ⟩

⟨ a,b⟩+⟨ c,d⟩=⟨ a+c,b+d⟩

⟨ 2+2,- 1+(-3) ⟩

a+(- b)=a-b

⟨ 2+2,- 1-3 ⟩

Add and subtract terms

⟨ 4, - 4 ⟩

Subchapter links

Exercises p.687-690