If the vector A = (a, b) is perpendicular to B = (b, -a), what is the relationsh

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Question: If the vector A = (a, b) is perpendicular to B = (b, -a), what is the relationship between a and b?

Options:

Correct Answer: a = -b

Solution:

A·B = ab - ab = 0, hence A and B are perpendicular if a = -b.

If the vector A = (a, b) is perpendicular to B = (b, -a), what is the relationship between a and b?

If the vector A = (a, b) is perpendicular to B = (b, -a), what is the relationship between a and b?

Step 1: Understand that two vectors are perpendicular if their dot product is zero.
Step 2: Write down the vectors: A = (a, b) and B = (b, -a).
Step 3: Calculate the dot product of A and B: A·B = a * b + b * (-a).
Step 4: Simplify the dot product: A·B = ab - ab.
Step 5: Notice that ab - ab equals 0, which means A·B = 0.
Step 6: Since the dot product is zero, A and B are perpendicular.
Step 7: From the calculation, we see that the relationship between a and b is that a must equal -b.

Dot Product – The dot product of two vectors is zero if and only if the vectors are perpendicular.
Perpendicular Vectors – Two vectors are perpendicular if the angle between them is 90 degrees, which can be determined using the dot product.
Algebraic Manipulation – Solving for relationships between variables using algebraic equations.