Understanding and Calculating the Resultant Vector of Three Given Vectors using TI-84 Calculator

Understanding vector addition is a fundamental concept in physics and engineering, often used in fields such as mechanics, navigation, and electronics. Let's explore the process of finding the resultant vector of the given vectors A, B, and C, and how to use a TI-84 calculator to simplify the calculation.

Given Vectors

Three vectors are provided as follows:

A 1ī - 3? B 2ī - ? C 3ī - 5?

Adding Vectors Component-wise

To find the resultant vector, we need to add the corresponding components of each vector. This means we add the i-components together and the j-components together separately.

Step 1: Adding the i-components

Ai 1

Bi 2

Ci 3

Sum of i-components: 1 2 3 6

Step 2: Adding the j-components

Aj -3

Bj -1

Cj -5

Sum of j-components: -3 - 1 - 5 -9

Therefore, the resultant vector R is:

R 6ī - 9?

Using the TI-84 Calculator for Vector Addition

If you have a TI-84 calculator, you can use it to perform these calculations more efficiently. Here’s how:

Method 1: Adding Vectors Component-wise

Set your calculator's mode to abi. This can be done by pressing [MODE] and selecting option 2 (Complex Format). Add the vectors by inputting the values directly. For the given vectors, you would input: 1i - 3i 2i - 1i 3i - 5i Press [ENTER] and the calculator should display the result as 6i - 7i.

Note: The text shown above assumes that the j-components are also added to -7 instead of -9, which is an error in the calculation. Correcting the j-component sum gives us the resultant vector R as 6ī - 9?.

Method 2: Calculating Magnitude and Direction

Set your calculator's mode to reθi. You can do this by selecting option 3 (Polar Format) in the [MODE] menu. Input the resultant vector in the form 6i - 7i. Press [ENTER] and you should get the magnitude and angle of the resultant vector.

The output will be approximately:

9.219544457e0i (9.22 at 0°)

Correcting the angle, the resultant vector R is 9.22 at 49.4°.

Conclusion

Understanding how to add vectors and use a TI-84 calculator can save time and reduce errors in calculations. By breaking down the problem into component-wise addition and using the calculator for efficient computation, you can quickly obtain the resultant vector.

Key Takeaways:

The resultant vector is found by summing the i and j components separately. The TI-84 calculator can make these calculations easier, whether in abi or reθi mode. The resultant vector sum is R 6ī - 9?.

Next Steps:

Further study on vector operations Prerequisite knowledge for vector-based fields like physics and engineering Exploring more complex vector problems on your TI-84 calculator