Find the scalar product of the vectors (3, -2, 5) and (1, 4, -1).

Find the scalar product of the vectors (3, -2, 5) and (1, 4, -1).

Step 1: Identify the two vectors. The first vector is (3, -2, 5) and the second vector is (1, 4, -1).
Step 2: Multiply the first component of the first vector (3) by the first component of the second vector (1). This gives 3 * 1 = 3.
Step 3: Multiply the second component of the first vector (-2) by the second component of the second vector (4). This gives -2 * 4 = -8.
Step 4: Multiply the third component of the first vector (5) by the third component of the second vector (-1). This gives 5 * -1 = -5.
Step 5: Add the results from Steps 2, 3, and 4 together: 3 + (-8) + (-5).
Step 6: Calculate the sum: 3 - 8 = -5, and then -5 - 5 = -10.
Step 7: The final result is the scalar product, which is -10.

Scalar Product – The scalar product (or dot product) of two vectors is calculated by multiplying their corresponding components and summing the results.