If A = ai + bj and B = ci + dj, what is the expression for A · B?

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Question: If A = ai + bj and B = ci + dj, what is the expression for A · B?

Options:

Correct Answer: ac + bd

Solution:

A · B = (ai + bj) · (ci + dj) = ac + bd.

If A = ai + bj and B = ci + dj, what is the expression for A · B?

If A = ai + bj and B = ci + dj, what is the expression for A · B?

Step 1: Identify the vectors A and B. A = ai + bj and B = ci + dj.
Step 2: Understand that the dot product (A · B) involves multiplying the corresponding components of the vectors.
Step 3: Multiply the 'i' components: a (from A) and c (from B) to get ac.
Step 4: Multiply the 'j' components: b (from A) and d (from B) to get bd.
Step 5: Add the results from Step 3 and Step 4 together: ac + bd.
Step 6: Write the final expression for the dot product: A · B = ac + bd.

Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Notation – Understanding the representation of vectors in terms of their components along the i and j axes.