If vector K = 2i + 2j and vector L = -i + 3j, what is the resultant vector K + L

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Question: If vector K = 2i + 2j and vector L = -i + 3j, what is the resultant vector K + L?

Options:

Correct Answer: i + 5j

Solution:

K + L = (2i + 2j) + (-i + 3j) = (2 - 1)i + (2 + 3)j = 1i + 5j = i + 5j.

If vector K = 2i + 2j and vector L = -i + 3j, what is the resultant vector K + L?

If vector K = 2i + 2j and vector L = -i + 3j, what is the resultant vector K + L?

Step 1: Identify vector K, which is given as 2i + 2j.
Step 2: Identify vector L, which is given as -i + 3j.
Step 3: Write down the expression for the resultant vector K + L, which is (2i + 2j) + (-i + 3j).
Step 4: Combine the i components: 2i + (-i) = (2 - 1)i = 1i.
Step 5: Combine the j components: 2j + 3j = (2 + 3)j = 5j.
Step 6: Write the resultant vector as 1i + 5j.
Step 7: Simplify the notation: 1i can be written as i, so the final answer is i + 5j.

Vector Addition – Understanding how to add vectors by combining their respective components.
Component-wise Calculation – Performing arithmetic operations on the i and j components separately.