Given vectors A = 4i + 2j and B = -i + 3j, calculate A · B.
Practice Questions
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Given vectors A = 4i + 2j and B = -i + 3j, calculate A · B.
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Questions & Step-by-Step Solutions
Given vectors A = 4i + 2j and B = -i + 3j, calculate A · B.
Step 1: Identify the components of vector A. A = 4i + 2j means A has a component of 4 in the i direction and 2 in the j direction.
Step 2: Identify the components of vector B. B = -i + 3j means B has a component of -1 in the i direction and 3 in the j direction.
Step 3: Write down the formula for the dot product of two vectors. The dot product A · B is calculated as (A_i * B_i) + (A_j * B_j), where A_i and A_j are the components of A, and B_i and B_j are the components of B.
Step 4: Substitute the components into the formula. A · B = (4 * -1) + (2 * 3).
Step 5: Calculate the first part: 4 * -1 = -4.
Step 6: Calculate the second part: 2 * 3 = 6.
Step 7: Add the results from Step 5 and Step 6: -4 + 6 = 2.
Step 8: The final result of A · B is 2.
Dot Product of Vectors – The dot product of two vectors A and B is calculated by multiplying their corresponding components and summing the results.
