If the vectors A = 5i + 5j and B = 5i - 5j, what is the scalar product A · B?

₹0.0

Question: If the vectors A = 5i + 5j and B = 5i - 5j, what is the scalar product A · B?

Options:

Correct Answer: 0

Solution:

A · B = (5)(5) + (5)(-5) = 25 - 25 = 0.

If the vectors A = 5i + 5j and B = 5i - 5j, what is the scalar product A · B?

If the vectors A = 5i + 5j and B = 5i - 5j, what is the scalar product A · B?

Step 1: Identify the components of vector A. A = 5i + 5j means A has a component of 5 in the i direction and 5 in the j direction.
Step 2: Identify the components of vector B. B = 5i - 5j means B has a component of 5 in the i direction and -5 in the j direction.
Step 3: Write down the formula for the scalar product (dot product) of two vectors. The formula is A · B = (A_i * B_i) + (A_j * B_j).
Step 4: Substitute the components of A and B into the formula. A · B = (5 * 5) + (5 * -5).
Step 5: Calculate the first part: 5 * 5 = 25.
Step 6: Calculate the second part: 5 * -5 = -25.
Step 7: Add the results from Step 5 and Step 6: 25 + (-25) = 25 - 25.
Step 8: Simplify the result: 25 - 25 = 0.

Vector Operations – Understanding how to compute the scalar (dot) product of two vectors.
Component-wise Multiplication – Applying the formula for the dot product by multiplying corresponding components of the vectors.