body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

7. Vectors

Continue to next subchapter

Exercise 44 Page 689

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

⟨ 16, 2 ⟩

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. h-2f+g ⇓ ⟨ 2, - 3 ⟩ -2 ⟨ -4, -2 ⟩ + ⟨ 6,1 ⟩ Now we can simplify the expression by first multiplying by the scalar and then adding and subtracting the remaining terms.

⟨ 2,- 3 ⟩ -2 ⟨ -4, -2 ⟩ + ⟨ 6, 1 ⟩

▼

Simplify

Distribute the scalar

⟨ 2,- 3 ⟩ -⟨ 2(-4), 2(-2) ⟩ + ⟨ 6, 1 ⟩

a(- b)=- a * b

⟨ 2,- 3 ⟩ -⟨ - 8, - 4 ⟩ + ⟨ 6, 1 ⟩

⟨ a,b ⟩ -⟨ c,d⟩ =⟨ a-c,b-d⟩

⟨ 2- (-8),- 3-(-4) ⟩ + ⟨ 6, 1 ⟩

a-(- b)=a+b

⟨ 2+8,- 3+4 ⟩ + ⟨ 6, 1 ⟩

Add terms

⟨ 10,1 ⟩ + ⟨ 6, 1 ⟩

⟨ a,b⟩+⟨ c,d⟩=⟨ a+c,b+d⟩

⟨ 10+6,1+1 ⟩

Add terms

⟨ 16, 2 ⟩

Subchapter links

Exercises p.687-690