If A = 7i + 24j and B = 24i - 7j, calculate A · B.
Practice Questions
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If A = 7i + 24j and B = 24i - 7j, calculate A · B.
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Questions & Step-by-Step Solutions
If A = 7i + 24j and B = 24i - 7j, calculate A · B.
Step 1: Identify the components of vector A, which are 7i and 24j.
Step 2: Identify the components of vector B, which are 24i and -7j.
Step 3: Use the formula for the dot product A · B, which is (A_i * B_i) + (A_j * B_j).
Step 4: Multiply the i components: 7 (from A) * 24 (from B) = 168.
Step 5: Multiply the j components: 24 (from A) * -7 (from B) = -168.
Step 6: Add the results from Step 4 and Step 5: 168 + (-168) = 0.
Dot Product – The dot product of two vectors A and B is calculated by multiplying their corresponding components and summing the results.
Vector Components – Understanding the components of vectors in terms of i (horizontal) and j (vertical) directions is crucial for performing vector operations.
