TI-89 Calculator Vector Operations

The TI-89 is the graphing calculator I use the most.  It’s simple to use, really powerful and it can be a huge time saver, if you know how to use it.  In this multi-post series, we’ll cover the functions and techniques you need for engineering.  I’ll also give you some tips on how to save time by making some simple changes to how you input and use data.

Let’s get started with the TI-89 vector operations…

Magnitude (norm), unit vector, dot product and cross product operations are must know material in engineering.  These are used extensively in courses like Statics, Dynamics, Orbital Mechanics and many others.

Once you learn how to use the TI-89 built in functions for vector operations, you’ll save time and keep yourself from making those annoying calculation errors that can cost you valuable exam points.  Sounds good, right? Let’s get started!

Below you’ll find a video tutorial for each operation as well as the syntax for each function and an example showing the result of the calculation.

How to create a vector in the TI-89

use [x-component, y-component, z-component]

Example: Create the vector 1.5i+2.76j+4.89k

Type: [1.5, 2.76, 4.89]

Vector addition & subtraction

Example: Find (2.2i+5.4j-8.7k)+(4.2i-5.0j-3.1k)

Type: [2.2,5.4, -8.7] + [4.2, -5.0, -3.1]

Result:  [6.4, .4, -11.8]

Example: Find (2.2i+5.4j-8.7k)-(4.2i-5.0j-3.1k)

Type: [2.2,5.4, -8.7] – [4.2, -5.0, -3.1]

Result:  [-2, 10.4, -5.6]

Multiplication by a scalar

Example: Find 5*(7.62i+15.4j-5.34k)

Type: 5 x [7.62, 15.4, -5.34]

Result:  [38.1, 77, -26.7]

Magnitude (norm) of a vector

Use the matrix norm() function.  Hit the following buttons to get there:

Example: Find the magnitude of 3i+9j+7k

Select/type: norm([3,9,7])

Result:  11.7898

TI-89 MATH Matrix Vector Operations

Use the MATH Matrix Vector Operations menu to get to the following functions.  Get there by hitting the buttons:   2^nd – 5 – 4 – up arrow – choose option L: Vector Ops – right arrow

Unit vector

Function:  unitV()

Example: Find the unit vector of  2i+5j+4k

Select/type:  unitV([2,5,4])

Result:  [0.298142, 0.745356, 0.596285]

Dot product

Function:  dotP()

Example: Find the dot product of (2i+4j+8k) and (4i-5j-3k)

Select/type:  dotP([2,4,8],[4,-5,-3])

Result:  -36

Cross product

Function:  crossP()

Example: Find the cross product of (-1i+3j+8k) and (4i-7j+3k)

Type:  crossP([-1,3,8],[4,-7,3])

Result:  [65, 35, -5]

Storing Vectors in the TI-89

Those are the main vector operations you’ll need.  In addition to the built-in functions, you can also save a ton of time by storing your vectors so you can use them later.  This will keep you from having to type all your numbers in again which, of course, helps keep the calculation errors to a minimum.  Once you get used to using this feature you’ll never go back! Use the STO button to do this…

Button:  STO>

Example: Store the vector as letter a. Then use a to find 15*(4.3i-9.7j+3.2k)

[4.3, -9.7, 3.2] STO> ALPHA =        (Note: STO>, ALPHA, = are the buttons you need to push)

15 x a = [64.5, -145.5, 48]

Note:  To use a capital letter, hit the up arrow button directly above the ALPHA button after you hit ALPHA.  To get A for example you’d hit STO>    ALPHA    UP ARROW =

Solving Equations

In the next post, we’ll cover solving equations.  See you then!