Find the scalar product of the vectors A = (2, 3) and B = (4, -1).
Practice Questions
Q1
Find the scalar product of the vectors A = (2, 3) and B = (4, -1).
-1
5
10
11
Questions & Step-by-Step Solutions
Find the scalar product of the vectors A = (2, 3) and B = (4, -1).
Correct Answer: 5
Step 1: Identify the components of vector A, which are (2, 3). This means A has an x-component of 2 and a y-component of 3.
Step 2: Identify the components of vector B, which are (4, -1). This means B has an x-component of 4 and a y-component of -1.
Step 3: Multiply the x-components of A and B together. This is 2 (from A) multiplied by 4 (from B), which equals 8.
Step 4: Multiply the y-components of A and B together. This is 3 (from A) multiplied by -1 (from B), which equals -3.
Step 5: Add the results from Step 3 and Step 4 together. This is 8 (from Step 3) plus -3 (from Step 4), which equals 5.
Step 6: The final result, which is the scalar product of vectors A and B, is 5.
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.
