If A = (x, y) and B = (y, x), what is the scalar product A · B?
Practice Questions
Q1
If A = (x, y) and B = (y, x), what is the scalar product A · B?
x^2 + y^2
xy
x^2 - y^2
0
Questions & Step-by-Step Solutions
If A = (x, y) and B = (y, x), what is the scalar product A · B?
Correct Answer: 2xy
Step 1: Identify the components of vector A, which are x and y.
Step 2: Identify the components of vector B, which are y and x.
Step 3: Write the formula for the scalar product (dot product) of two vectors A and B: A · B = (x1 * y1) + (x2 * y2).
Step 4: Substitute the components of A and B into the formula: A · B = (x * y) + (y * x).
Step 5: Simplify the expression: A · B = xy + yx.
Step 6: Recognize that xy and yx are the same, so combine them: A · B = 2xy.
Scalar Product – The scalar product (or dot product) of two vectors A and B is calculated as the sum of the products of their corresponding components.
Vector Notation – Understanding the notation of vectors and how to manipulate them is crucial for solving problems involving vector operations.
