Given vectors P = (4, 0, -3) and Q = (1, 2, 1), find the scalar product P · Q.
Practice Questions
Q1
Given vectors P = (4, 0, -3) and Q = (1, 2, 1), find the scalar product P · Q.
-1
5
10
2
Questions & Step-by-Step Solutions
Given vectors P = (4, 0, -3) and Q = (1, 2, 1), find the scalar product P · Q.
Correct Answer: 1
Step 1: Identify the components of vector P, which are (4, 0, -3).
Step 2: Identify the components of vector Q, which are (1, 2, 1).
Step 3: Multiply the first component of P (which is 4) by the first component of Q (which is 1). This gives 4 * 1 = 4.
Step 4: Multiply the second component of P (which is 0) by the second component of Q (which is 2). This gives 0 * 2 = 0.
Step 5: Multiply the third component of P (which is -3) by the third component of Q (which is 1). This gives -3 * 1 = -3.
Step 6: Add the results from Steps 3, 4, and 5 together: 4 + 0 - 3.
Step 7: Calculate the final result: 4 + 0 - 3 = 1.
Vector Scalar Product – The scalar product (or dot product) of two vectors is calculated by multiplying their corresponding components and summing the results.
