Which of the following vectors is orthogonal to the vector A = 2i + 3j?

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Question: Which of the following vectors is orthogonal to the vector A = 2i + 3j?

Options:

Correct Answer: 3i - 2j

Solution:

A vector is orthogonal if A · B = 0. For B = 3i - 2j, A · B = 6 - 6 = 0.

Which of the following vectors is orthogonal to the vector A = 2i + 3j?

Which of the following vectors is orthogonal to the vector A = 2i + 3j?

Step 1: Understand what orthogonal means. Two vectors are orthogonal if their dot product is zero.
Step 2: Identify the given vector A, which is A = 2i + 3j.
Step 3: Write down the vector B that you want to check for orthogonality. In this case, B = 3i - 2j.
Step 4: Calculate the dot product of A and B. The dot product is calculated as A · B = (2 * 3) + (3 * -2).
Step 5: Perform the multiplication: 2 * 3 = 6 and 3 * -2 = -6.
Step 6: Add the results of the multiplication: 6 + (-6) = 0.
Step 7: Since the dot product A · B equals 0, conclude that the vector B = 3i - 2j is orthogonal to vector A.

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