Question: What is the scalar triple product of vectors A = (1, 0, 0), B = (0, 1, 0), C = (0, 0, 1)?
Options:
1
0
-1
2
Correct Answer: 1
Solution:
Scalar triple product = A · (B × C) = 1.
What is the scalar triple product of vectors A = (1, 0, 0), B = (0, 1, 0), C = (
Practice Questions
Q1
What is the scalar triple product of vectors A = (1, 0, 0), B = (0, 1, 0), C = (0, 0, 1)?
1
0
-1
2
Questions & Step-by-Step Solutions
What is the scalar triple product of vectors A = (1, 0, 0), B = (0, 1, 0), C = (0, 0, 1)?
Step 1: Identify the vectors A, B, and C. Here, A = (1, 0, 0), B = (0, 1, 0), and C = (0, 0, 1).
Step 2: Calculate the cross product of vectors B and C. The cross product B × C is calculated as follows: B × C = |i j k| |0 1 0| |0 0 1| = (1*1 - 0*0)i - (0*1 - 0*0)j + (0*0 - 0*0)k = (1, 0, 0).
Step 3: Now, we need to calculate the dot product of vector A with the result from Step 2. A · (B × C) = (1, 0, 0) · (1, 0, 0).
Step 4: Calculate the dot product: A · (B × C) = 1*1 + 0*0 + 0*0 = 1.
Step 5: The scalar triple product is the result from Step 4, which is 1.
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