Calculate the scalar product of the vectors (2, 3, 4) and (4, 3, 2).

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Question: Calculate the scalar product of the vectors (2, 3, 4) and (4, 3, 2).

Options:

Correct Answer: 28

Solution:

Scalar product = 2*4 + 3*3 + 4*2 = 8 + 9 + 8 = 25.

Calculate the scalar product of the vectors (2, 3, 4) and (4, 3, 2).

Calculate the scalar product of the vectors (2, 3, 4) and (4, 3, 2).

Step 1: Identify the two vectors. The first vector is (2, 3, 4) and the second vector is (4, 3, 2).
Step 2: Multiply the first component of the first vector (2) by the first component of the second vector (4). This gives 2 * 4 = 8.
Step 3: Multiply the second component of the first vector (3) by the second component of the second vector (3). This gives 3 * 3 = 9.
Step 4: Multiply the third component of the first vector (4) by the third component of the second vector (2). This gives 4 * 2 = 8.
Step 5: Add all the results from Steps 2, 3, and 4 together: 8 + 9 + 8.
Step 6: Calculate the total: 8 + 9 = 17, and then 17 + 8 = 25.

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