TI-89 Vector Operations
Your calculator uses square brackets [ ] to indicate that you are operating with a vector. To enter a vector 3i + 2j + 5k, type [3, 2, 5] ENTER
The basic operations that can be performed with vectors are addition, subtraction, and scalar multiplication.
For example, to add (3i + 2j + 5k) + (7i - 2j + 8k), type
[3, 2, 5] + [7, -2, 8] ENTER
To perform the scalar multiplication 9(3i + 2j +5k), type
9 [3, 2, 5] ENTER
Standard multiplication, division, and exponent are not allowed with vectors. There are a series of special commands that can be performed with vectors. These commands can be found on the MATH → Matrix → Vector ops menu (2ND 5, 4,alpha L). These operations are
unitV( Creates a unit vector crossP( Cross Product dotP( Dot Product Converts 2 dimensional vectors from Rectangular to Polar → Rect Converts 2 dimensional vectors from Polar to Rectangular → Cylind Converts 3 dimensional vectors from Rectangular to Cylindrical → Sphere
(finds magnitude in 3 dimensions)
Converts 3 dimensional vectors from Rectangular to Spherical
To save a vector as a variable, create the vector using the [ ] notation, pres STO → followed by the vector name and the ENTER
There are a series of special commands that can be performed with vectors. These commands can be found on the MATH → Matrix → Vector ops menu (2ND 5, 4,alpha L).
Creating a Unit Vector
A unit vector is a vector with magnitude equal to one (1). This is accomplished by dividing the vector by its magnitude. On the calculator, this is accomplished through the unitV command. The unitV command is found under MATH → Matrix → Vector ops.
For example, to find a unit vector in the direction of 3i + 2j + 5k, use
unitV( [3, 2, 5] ) ENTER.
If your answer flows off the screen, use the cursor keys to see the entire vector.
Dot and Cross Products
To find the Dot or Cross product of two vectors, go the MATH → Matrix → Vector ops menu and choose the appropriate item for Cross or Dot product.
If you have stored two vectors, called VEC1 and VEC2, find the cross product by pressing crossP(VEC1,VEC2), and press ENTER.
If you have not stored your vectors, press crossP( followed by your vectors. For example, to find the cross product of (3i + 2j + 5k) and (7i - 2j + 8k), press
crossP( [3, 2, 5] , [7, -2, 8] ) ENTER
In engineering courses, it is often useful to convert from rectangular coordinates to another coordinate system. The TI 89 can convert two dimensional vectors between polar and rectangular coordinates and can convert 3 dimensional vectors between rectangular, cylindrical and spherical coordinates. The calculator will use either radians or degrees, whichever is the current mode.
In general, all conversions can be found in the MATH → Matrix → Vector ops menu.
Rectangular to Polar Conversions
To convert the vector 3i + 4j into polar coordinates, enter
[3, 4] → Polar ENTER
Using degree mode, this gives the polar vector
[5, ∠ 53.13]
This indicates that the magnitude of the vector is 5 and that the angle is approximately 53.13 degrees. If your mode is set in radians, the angle is approximately 0.92 radians.
Entering an Angle
The angle symbol is found on the left side of the keypad, two buttons above the ON button. Be sure to press 2ND to access the angle symbol.
Polar to Rectangular Conversions
To convert a vector with magnitude 7 and an angle of 130 degrees into rectangular, press
[7, ∠130] → Rect ENTER
Other vector conversions are accomplished in similar fashion.
The conversion to spherical is useful when determining the magnitude of a three dimensional vector.
When working with spherical coordinates, it is important to remember that the first angle is theta and the second angle is phi.