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Considering a coordinate system in space, in a previously defined orientation, and knowing that the vectors (orthogonal to each other) corresponding to the X and Y axes are known, what is the name of the operation that is capable of producing the vector corresponding to the Z axis of this system - that is, perpendicular to the other two?
Real Exam
Community
DDanyel
A
Scalar product.
B
Vector product.
C
Normalization.
D
Translation.
E
Projection.
Explanation:
Explanation
The correct answer is B) Vector product (also known as cross product).
Why this is correct:
- Vector product (cross product) of two vectors produces a third vector that is perpendicular to both original vectors.
- In a 3D coordinate system, if you have orthogonal unit vectors for X and Y axes, the cross product of X × Y gives you the Z axis vector.
- This follows the right-hand rule convention for coordinate systems.
Why other options are incorrect:
- A) Scalar product: Produces a scalar value, not a vector.
- C) Normalization: Converts a vector to unit length but doesn't change its direction.
- D) Translation: Moves points or vectors in space but doesn't create perpendicular vectors.
- E) Projection: Finds the component of one vector along another vector's direction.
Mathematical Context:
In linear algebra and 3D geometry, the cross product is specifically designed to find a vector perpendicular to two given vectors. For orthogonal unit vectors (X-axis) and (Y-axis), (Z-axis).
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