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Find the scalar product of the vectors A = 5i + 12j and B = 3i - 4j.
Find the scalar product of the vectors A = 5i + 12j and B = 3i - 4j.
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Practice Questions
1 question
Q1
Find the scalar product of the vectors A = 5i + 12j and B = 3i - 4j.
-33
33
39
45
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A · B = (5)(3) + (12)(-4) = 15 - 48 = -33.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the scalar product of the vectors A = 5i + 12j and B = 3i - 4j.
Solution:
A · B = (5)(3) + (12)(-4) = 15 - 48 = -33.
Steps: 6
Show Steps
Step 1: Identify the components of vector A. A = 5i + 12j means A has a component of 5 in the i direction and 12 in the j direction.
Step 2: Identify the components of vector B. B = 3i - 4j means B has a component of 3 in the i direction and -4 in the j direction.
Step 3: Multiply the i components of A and B. This is 5 (from A) times 3 (from B), which equals 15.
Step 4: Multiply the j components of A and B. This is 12 (from A) times -4 (from B), which equals -48.
Step 5: Add the results from Step 3 and Step 4 together. This is 15 + (-48), which equals -33.
Step 6: The final result, -33, is the scalar product of vectors A and B.
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