Find the scalar product of vectors A = 7i + 1j + 2k and B = 3i + 4j + 5k.

Find the scalar product of vectors A = 7i + 1j + 2k and B = 3i + 4j + 5k.

Step 1: Identify the components of vector A, which are A = 7i + 1j + 2k. This means A has 7 in the i direction, 1 in the j direction, and 2 in the k direction.
Step 2: Identify the components of vector B, which are B = 3i + 4j + 5k. This means B has 3 in the i direction, 4 in the j direction, and 5 in the k direction.
Step 3: Multiply the corresponding components of vectors A and B. For the i components, multiply 7 (from A) by 3 (from B): 7 * 3 = 21.
Step 4: For the j components, multiply 1 (from A) by 4 (from B): 1 * 4 = 4.
Step 5: For the k components, multiply 2 (from A) by 5 (from B): 2 * 5 = 10.
Step 6: Add all the results from the multiplications together: 21 + 4 + 10.
Step 7: Calculate the final sum: 21 + 4 = 25, and then 25 + 10 = 35.
Step 8: The scalar product of vectors A and B is 35.

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, j, and k components is essential for performing operations like the scalar product.