Find the scalar product of A = 6i + 8j and B = 2i + 3j.

Find the scalar product of A = 6i + 8j and B = 2i + 3j.

Step 1: Identify the components of vector A. A = 6i + 8j means A has a component of 6 in the i direction and 8 in the j direction.
Step 2: Identify the components of vector B. B = 2i + 3j means B has a component of 2 in the i direction and 3 in the j direction.
Step 3: Multiply the i components of A and B together. This is 6 (from A) times 2 (from B), which equals 12.
Step 4: Multiply the j components of A and B together. This is 8 (from A) times 3 (from B), which equals 24.
Step 5: Add the results from Step 3 and Step 4 together. This is 12 + 24, which equals 36.
Step 6: The final result, 36, 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.