If the vectors A = 6i + 8j and B = 3i + 4j are perpendicular, what is the value

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Question: If the vectors A = 6i + 8j and B = 3i + 4j are perpendicular, what is the value of A · B? (2021)

Options:

Correct Answer: 0

Exam Year: 2021

Solution:

A · B = (6)(3) + (8)(4) = 18 + 32 = 50, but since they are perpendicular, A · B = 0.

If the vectors A = 6i + 8j and B = 3i + 4j are perpendicular, what is the value of A · B? (2021)

If the vectors A = 6i + 8j and B = 3i + 4j are perpendicular, what is the value of A · B? (2021)

Step 1: Understand that two vectors are perpendicular if their dot product is zero.
Step 2: Identify the vectors given in the question: A = 6i + 8j and B = 3i + 4j.
Step 3: Calculate the dot product A · B using the formula: A · B = (A_x * B_x) + (A_y * B_y).
Step 4: Substitute the values: A_x = 6, A_y = 8, B_x = 3, B_y = 4.
Step 5: Perform the multiplication: (6 * 3) + (8 * 4).
Step 6: Calculate 6 * 3 = 18 and 8 * 4 = 32.
Step 7: Add the results: 18 + 32 = 50.
Step 8: Since the vectors are stated to be perpendicular, the dot product A · B must equal 0.

Dot Product of Vectors – The dot product of two vectors A and B is calculated as A · B = |A||B|cos(θ), where θ is the angle between the vectors. If the vectors are perpendicular, θ = 90 degrees, and thus A · B = 0.
Perpendicular Vectors – Two vectors are perpendicular if their dot product equals zero.