If I = (1, 2, 3) and J = (4, 5, 6), calculate I · J.

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Question: If I = (1, 2, 3) and J = (4, 5, 6), calculate I · J.

Options:

Correct Answer: 30

Solution:

I · J = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32.

If I = (1, 2, 3) and J = (4, 5, 6), calculate I · J.

If I = (1, 2, 3) and J = (4, 5, 6), calculate I · J.

Step 1: Identify the components of vector I, which are 1, 2, and 3.
Step 2: Identify the components of vector J, which are 4, 5, and 6.
Step 3: Multiply the first component of I (1) by the first component of J (4). This gives 1 * 4 = 4.
Step 4: Multiply the second component of I (2) by the second component of J (5). This gives 2 * 5 = 10.
Step 5: Multiply the third component of I (3) by the third component of J (6). This gives 3 * 6 = 18.
Step 6: Add the results from Steps 3, 4, and 5 together: 4 + 10 + 18.
Step 7: Calculate the total: 4 + 10 = 14, then 14 + 18 = 32.

Dot Product – The dot product of two vectors is calculated by multiplying corresponding components and summing the results.