Final answer:
To find the combined vector of i^ - 3j^ + 2k^ and 3i^ - k^ + 5j^ - 4k^, we add the corresponding components to get 4i^ + 2j^ - 3k^. Without a desired result vector, we cannot find a specific vector to add to this sum.
Step-by-step explanation:
The student is asking to find the vector that must be added to the sum of the vectors i^ - 3j^ + 2k^ and 3i^ - k^ + 5j^ - 4k^. To solve this, we need to perform vector addition. Here is the solution step by step:
- Firstly, we sum up the corresponding components of the vectors. For the i components, we have 1 + 3 = 4i^. For the j components, -3 + 5 = 2j^. For the k components, 2 - 4 - 1 = -3k^.
- Combining these results, we get a new vector 4i^ + 2j^ - 3k^.
- This new vector represents the combined effect of the original two vectors.
To find the vector that we must add to this sum to achieve a certain result, more information is needed about the desired result. Without this target result, we cannot determine what vector needs to be added.