Calculate the scalar product of the vectors A = (4, -1, 2) and B = (2, 3, 1).
Practice Questions
Q1
Calculate the scalar product of the vectors A = (4, -1, 2) and B = (2, 3, 1).
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Questions & Step-by-Step Solutions
Calculate the scalar product of the vectors A = (4, -1, 2) and B = (2, 3, 1).
Correct Answer: 7
Step 1: Identify the components of vector A, which are (4, -1, 2).
Step 2: Identify the components of vector B, which are (2, 3, 1).
Step 3: Multiply the first component of A (4) by the first component of B (2). This gives 4 * 2 = 8.
Step 4: Multiply the second component of A (-1) by the second component of B (3). This gives -1 * 3 = -3.
Step 5: Multiply the third component of A (2) by the third component of B (1). This gives 2 * 1 = 2.
Step 6: Add the results from Steps 3, 4, and 5 together: 8 + (-3) + 2.
Step 7: Calculate the sum: 8 - 3 + 2 = 7.
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 identify and use the components of vectors in calculations.
