If A = 2i - j and B = -i + 3j, what is the value of A · B?

If A = 2i - j and B = -i + 3j, what is the value of A · B?

Step 1: Identify the components of vector A. A = 2i - j means A has a component of 2 in the i direction and -1 in the j direction.
Step 2: Identify the components of vector B. B = -i + 3j means B has a component of -1 in the i direction and 3 in the j direction.
Step 3: Write down the formula for the dot product A · B. The dot product is calculated as (A_i * B_i) + (A_j * B_j), where A_i and A_j are the components of A, and B_i and B_j are the components of B.
Step 4: Substitute the values into the formula. A · B = (2 * -1) + (-1 * 3).
Step 5: Calculate the first part: 2 * -1 = -2.
Step 6: Calculate the second part: -1 * 3 = -3.
Step 7: Add the results from Step 5 and Step 6: -2 + (-3) = -2 - 3 = -5.
Step 8: Conclude that the value of A · B is -5.

Dot Product of Vectors – The dot product of two vectors A and B is calculated by multiplying their corresponding components and summing the results.