Given vectors P = (4, 1, 0) and Q = (0, 2, 3), find the scalar product P · Q.
Practice Questions
Q1
Given vectors P = (4, 1, 0) and Q = (0, 2, 3), find the scalar product P · Q.
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Questions & Step-by-Step Solutions
Given vectors P = (4, 1, 0) and Q = (0, 2, 3), find the scalar product P · Q.
Step 1: Identify the components of vector P, which are (4, 1, 0).
Step 2: Identify the components of vector Q, which are (0, 2, 3).
Step 3: Multiply the first component of P (which is 4) by the first component of Q (which is 0). This gives 4 * 0 = 0.
Step 4: Multiply the second component of P (which is 1) by the second component of Q (which is 2). This gives 1 * 2 = 2.
Step 5: Multiply the third component of P (which is 0) by the third component of Q (which is 3). This gives 0 * 3 = 0.
Step 6: Add the results from Steps 3, 4, and 5 together: 0 + 2 + 0 = 2.
Step 7: The scalar product P · Q is 2.
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.
