If the vector a = (2, 3) and b = (4, 1), what is the resultant vector a + b?

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Question: If the vector a = (2, 3) and b = (4, 1), what is the resultant vector a + b?

Options:

Correct Answer: (6, 4)

Solution:

Resultant vector a + b = (2+4, 3+1) = (6, 4).

If the vector a = (2, 3) and b = (4, 1), what is the resultant vector a + b?

If the vector a = (2, 3) and b = (4, 1), what is the resultant vector a + b?

Step 1: Identify the components of vector a. Vector a = (2, 3) means it has an x-component of 2 and a y-component of 3.
Step 2: Identify the components of vector b. Vector b = (4, 1) means it has an x-component of 4 and a y-component of 1.
Step 3: Add the x-components of both vectors. 2 (from vector a) + 4 (from vector b) = 6.
Step 4: Add the y-components of both vectors. 3 (from vector a) + 1 (from vector b) = 4.
Step 5: Combine the results from Step 3 and Step 4 to form the resultant vector. The resultant vector a + b = (6, 4).

Vector Addition – The process of adding two vectors by adding their corresponding components.