Find the scalar product of the vectors A = 5i + 12j and B = 3i - 4j.

Find the scalar product of the vectors A = 5i + 12j and B = 3i - 4j.

Step 1: Identify the components of vector A. A = 5i + 12j means A has a component of 5 in the i direction and 12 in the j direction.
Step 2: Identify the components of vector B. B = 3i - 4j means B has a component of 3 in the i direction and -4 in the j direction.
Step 3: Multiply the i components of A and B. This is 5 (from A) times 3 (from B), which equals 15.
Step 4: Multiply the j components of A and B. This is 12 (from A) times -4 (from B), which equals -48.
Step 5: Add the results from Step 3 and Step 4 together. This is 15 + (-48), which equals -33.
Step 6: The final result, -33, is the scalar product of vectors A and B.

Scalar Product – The scalar product (or dot product) of two vectors is calculated by multiplying their corresponding components and summing the results.
Vector Components – Understanding how to break down vectors into their i (x-axis) and j (y-axis) components is essential for calculating the scalar product.