Answer :
Final answer:
The quantity 3v + 5w is 4j - 6k.
Explanation:
To find the quantity 3v + 5w, we need to multiply each component of v by 3 and each component of w by 5, and then add the corresponding components together.
Given:
- v = 5i - 2j + 3k
- w = -3i + 2j - 3k
Multiplying each component of v by 3:
- 3v = 3(5i) - 3(2j) + 3(3k)
- 3v = 15i - 6j + 9k
Multiplying each component of w by 5:
- 5w = 5(-3i) + 5(2j) - 5(3k)
- 5w = -15i + 10j - 15k
Adding the corresponding components together:
- 3v + 5w = (15i - 6j + 9k) + (-15i + 10j - 15k)
- 3v + 5w = (15i - 15i) + (-6j + 10j) + (9k - 15k)
- 3v + 5w = 0i + 4j - 6k
Therefore, 3v + 5w = 4j - 6k.
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