If vector A = 4i + 3j and vector B = -i + 2j, what is the resultant vector A + B

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Question: If vector A = 4i + 3j and vector B = -i + 2j, what is the resultant vector A + B? (2019)

Options:

Correct Answer: 3i + 5j

Exam Year: 2019

Solution:

A + B = (4 - 1)i + (3 + 2)j = 3i + 5j.

If vector A = 4i + 3j and vector B = -i + 2j, what is the resultant vector A + B? (2019)

If vector A = 4i + 3j and vector B = -i + 2j, what is the resultant vector A + B? (2019)

Step 1: Identify the components of vector A. Vector A = 4i + 3j means it has a component of 4 in the i direction and 3 in the j direction.
Step 2: Identify the components of vector B. Vector B = -i + 2j means it has a component of -1 in the i direction and 2 in the j direction.
Step 3: Add the i components of both vectors. For vector A, the i component is 4, and for vector B, the i component is -1. So, 4 + (-1) = 4 - 1 = 3.
Step 4: Add the j components of both vectors. For vector A, the j component is 3, and for vector B, the j component is 2. So, 3 + 2 = 5.
Step 5: Combine the results from Step 3 and Step 4 to form the resultant vector. The resultant vector A + B = 3i + 5j.

Vector Addition – Understanding how to add vectors by combining their respective components.