Question: If vectors A = 3i + 4j and B = 2i - j, what is the dot product A · B?
Options:
-1
2
10
11
Correct Answer: 10
Solution:
A · B = (3)(2) + (4)(-1) = 6 - 4 = 2.
If vectors A = 3i + 4j and B = 2i - j, what is the dot product A · B?
Practice Questions
Q1
If vectors A = 3i + 4j and B = 2i - j, what is the dot product A · B?
-1
2
10
11
Questions & Step-by-Step Solutions
If vectors A = 3i + 4j and B = 2i - j, what is the dot product A · B?
Step 1: Identify the components of vector A. A = 3i + 4j means A has a component of 3 in the i direction and 4 in the j direction.
Step 2: Identify the components of vector B. B = 2i - j means B has a component of 2 in the i direction and -1 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's i component * B's i component) + (A's j component * B's j component).
Step 4: Substitute the components of A and B into the formula. This gives us (3 * 2) + (4 * -1).
Step 5: Calculate the products. First, calculate 3 * 2 = 6. Then calculate 4 * -1 = -4.
Step 6: Add the results from Step 5. So, 6 + (-4) = 6 - 4 = 2.
Step 7: The final result of the dot product A · B is 2.
Dot Product of Vectors – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
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