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

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

Options:

Correct Answer: i + 7j

Solution:

R = A + B = (2 - 1)i + (3 + 4)j = 1i + 7j.

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

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

Step 1: Identify the components of vector A. Vector A = 2i + 3j means it has a component of 2 in the i direction and 3 in the j direction.
Step 2: Identify the components of vector B. Vector B = -i + 4j means it has a component of -1 in the i direction and 4 in the j direction.
Step 3: Add the i components of both vectors. For vector A, the i component is 2, and for vector B, the i component is -1. So, 2 + (-1) = 2 - 1 = 1.
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 4. So, 3 + 4 = 7.
Step 5: Combine the results from Step 3 and Step 4 to form the resultant vector R. R = 1i + 7j.

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