Find the scalar product of A = 2i + 3j + k and B = i + 2j + 3k. (2020)

Find the scalar product of A = 2i + 3j + k and B = i + 2j + 3k. (2020)

Step 1: Identify the components of vector A. A = 2i + 3j + k means A has components: A_x = 2, A_y = 3, A_z = 1.
Step 2: Identify the components of vector B. B = i + 2j + 3k means B has components: B_x = 1, B_y = 2, B_z = 3.
Step 3: Use the formula for the scalar product (dot product) of two vectors: A · B = (A_x * B_x) + (A_y * B_y) + (A_z * B_z).
Step 4: Substitute the components into the formula: A · B = (2 * 1) + (3 * 2) + (1 * 3).
Step 5: Calculate each term: (2 * 1) = 2, (3 * 2) = 6, (1 * 3) = 3.
Step 6: Add the results together: 2 + 6 + 3 = 11.
Step 7: The scalar product of A and B is 11.

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 the components of vectors in terms of unit vectors i, j, and k is essential for performing operations like the scalar product.