No, the question really states: ##|\vec{AC}| .| \vec{BD}|## so I interpret it as product of magnitude of vector AC and BDharuspex said:Your question as stated does not involve a dot product. Did you mean ##|\vec{AC}.\vec{BD}|##?
Oh ok, I see your point.Also, as stated, it clearly is unsolvable. You could easily vary |AC| while keeping |BD| fixed. Not sure yet if changing it to the dot product of the vectors resolves that.
The product of two magnitude of vectors is a mathematical operation that results in a scalar quantity. It is calculated by multiplying the magnitudes of two vectors and then taking the cosine of the angle between them.
The product of two magnitude of vectors is different from the dot product because it only takes into account the magnitudes of the vectors, while the dot product also considers the direction of the vectors.
Yes, the product of two magnitude of vectors can be negative if the angle between the two vectors is greater than 90 degrees. This indicates that the two vectors are pointing in opposite directions.
The product of two magnitude of vectors is commonly used in physics to calculate the work done by a force on an object. It is also used in calculating torque, which is the rotational equivalent of force.
Yes, the product of two magnitude of vectors has various real-life applications. It is used in engineering and design to calculate the force needed to move objects, in navigation to determine the direction and speed of an object, and in computer graphics to create 3D models and animations.