If the vectors A = 2i + 3j and B = 3i + 4j are perpendicular, what is the value

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Question: If the vectors A = 2i + 3j and B = 3i + 4j are perpendicular, what is the value of A · B?

Options:

Correct Answer: 0

Solution:

Since A and B are perpendicular, A · B = 0.

If the vectors A = 2i + 3j and B = 3i + 4j are perpendicular, what is the value of A · B?

If the vectors A = 2i + 3j and B = 3i + 4j are perpendicular, what is the value of A · B?

Step 1: Understand that two vectors are perpendicular if the angle between them is 90 degrees.
Step 2: Recall that the dot product of two vectors A and B is given by A · B = |A| |B| cos(θ), where θ is the angle between them.
Step 3: Since A and B are perpendicular, the angle θ = 90 degrees.
Step 4: The cosine of 90 degrees is 0, so cos(90°) = 0.
Step 5: Therefore, A · B = |A| |B| cos(90°) = |A| |B| * 0 = 0.
Step 6: Conclude that if A and B are perpendicular, then A · B = 0.

Dot Product of Vectors – The dot product of two vectors is zero if and only if the vectors are perpendicular.
Vector Components – Understanding how to represent vectors in terms of their components (i and j) is crucial for calculating the dot product.