Final answer:
The vector C that satisfies the equation 2C - 2A + 3B = 0 is C = -5i - 3.5j + 3k.
Step-by-step explanation:
To find vector C such that 2C - 2A + 3B = 0, we first need to understand the vectors given. Vector A is 4i - 8j - 3k, and vector B is 6i - 3j - 4k. Now, we will rewrite the equation with variables:
2C - 2(4i - 8j - 3k) + 3(6i - 3j - 4k) = 0
Simplifying, we get:
2C - 8i + 16j + 6k + 18i - 9j - 12k = 0
Combining like terms:
2C + 10i + 7j - 6k = 0
Now, isolate C on one side:
2C = -10i - 7j + 6k
Dividing both sides by 2, we find:
C = -5i - 3.5j + 3k
So, vector C that satisfies 2C - 2A + 3B = 0 is -5i - 3.5j + 3k.