Math Problem Statement

Calculate the length of the following vectors in two different ways:

  • By using the Pythagorean Theorem
  • By using the dot product Tip: the angle between a vector and itself is 0, so cos(0°) = 1
  1. →a = (5, 4)
  2. →b = (-1, 3, 2)

Solution

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Math Problem Analysis

Mathematical Concepts

Vector Length
Pythagorean Theorem
Dot Product

Formulas

Vector length formula using Pythagorean Theorem: ||v|| = √(x^2 + y^2) for a 2D vector
Vector length formula using dot product: ||v|| = √(v · v)

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 10-12

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