Question: If A = (x, y, z) and B = (1, 1, 1), find the scalar product A · B.
Options:
x + y + z
x - y + z
x + y - z
x - y - z
Correct Answer: x + y + z
Solution:
A · B = x*1 + y*1 + z*1 = x + y + z.
If A = (x, y, z) and B = (1, 1, 1), find the scalar product A · B.
Practice Questions
Q1
If A = (x, y, z) and B = (1, 1, 1), find the scalar product A · B.
x + y + z
x - y + z
x + y - z
x - y - z
Questions & Step-by-Step Solutions
If A = (x, y, z) and B = (1, 1, 1), find the scalar product A · B.
Step 1: Identify the components of vector A, which are x, y, and z.
Step 2: Identify the components of vector B, which are 1, 1, and 1.
Step 3: Use the formula for the scalar product (dot product), which is A · B = (x1 * x2) + (y1 * y2) + (z1 * z2).
Step 4: Substitute the components of A and B into the formula: A · B = (x * 1) + (y * 1) + (z * 1).
Step 5: Simplify the expression: A · B = x + y + z.
Scalar Product – The scalar product (or dot product) of two vectors is calculated by multiplying their corresponding components and summing the results.
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