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ZingPath: Vector Operations

Vector Arithmetic with Coordinates

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Vector Operations

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Lesson Focus

Vector Arithmetic with Coordinates


Learning Made Easy

You will learn how to add and subtract two vectors, and multiply a vector by a scalar when given the coordinate representations of the vectors.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Add two vectors coordinate-wise given their coordinate representation.
  • Multiply a vector by a scalar coordinate-wise given their coordinate representation.
  • Subtract two vectors coordinate-wise given their coordinate representation.

Everything You'll Have Covered

Vector Addition:

Recall that a vector is a quantity consisting of both a magnitude and a direction. Consider a car that travels 50 miles due north, turns, and then travels east for 50 more miles. This situation is depicted below:

At the end of its journey, the car stops at the point (50, 50), which is approximately 70.71 miles from the car's starting point and in the northeast direction. This is a vector quantity, since it consists of both length (approximately 70.71 miles) and direction (northeast). It is known as the displacement vector and represents the length and direction of the shortest path between the starting and ending points. Note that displacement depends only on the starting and ending points. For example, if the car started at the origin and spiraled around it in increasingly large circles until reaching the destination (50, 50), the displacement vector is again (50, 50).

Vector Addition:

This geometric method of representating the sum of two vectors is known as the head-to-tail method. We can use it to find an algebraic definition of vector addition.

Tutorial Details

Approximate Time 20 Minutes
Pre-requisite Concepts Students should know the definition of vector, opposite vectors, and zero vector; be able to represent vectors in the coordinate plane with either directed line segments or coordinates; and know how to add, subtract, and multiply real numbers.
Course Algebra-2
Type of Tutorial Concept Development
Key Vocabulary adding vectors, multiplying vectors by a scalar, coordinates