If the scalar product of two vectors A and B is 0, what can be inferred about th
Practice Questions
Q1
If the scalar product of two vectors A and B is 0, what can be inferred about the vectors?
They are equal
They are parallel
They are orthogonal
They are collinear
Questions & Step-by-Step Solutions
If the scalar product of two vectors A and B is 0, what can be inferred about the vectors?
Step 1: Understand what a scalar product (dot product) is. It is a way to multiply two vectors to get a single number.
Step 2: Know that the scalar product of two vectors A and B is calculated as A · B = |A| * |B| * cos(θ), where θ is the angle between the two vectors.
Step 3: If A · B = 0, this means that the result of the scalar product is zero.
Step 4: The only way for the scalar product to be zero is if cos(θ) = 0.
Step 5: Cosine of an angle is zero when the angle θ is 90 degrees (or π/2 radians).
Step 6: Therefore, if A · B = 0, it means that the angle between vectors A and B is 90 degrees.
Step 7: When two vectors are at a 90-degree angle to each other, they are said to be orthogonal or perpendicular.
Scalar Product – The scalar product (or dot product) of two vectors is a measure of their directional alignment, calculated as A · B = |A| |B| cos(θ), where θ is the angle between the vectors.
Orthogonality – Two vectors are orthogonal if their scalar product is zero, indicating that they are at a right angle (90 degrees) to each other.
