Scelta multipla
Which of the following vectors is equal to the cross product ?
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3. Vectors
Introduction to Vectors
Scelta multipla
Given two vectors and as shown in Figure 2, what is the angle between them if points along the positive x-axis and points along the positive y-axis?
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Guida verificata passo dopo passo1
Identify the directions of the two vectors: vector \( \vec{e} \) points along the positive x-axis, and vector \( \vec{f} \) points along the positive y-axis.
Recall that the positive x-axis and positive y-axis are perpendicular to each other in a standard Cartesian coordinate system.
Understand that the angle \( \pi \) between two vectors is the measure of the smallest rotation from one vector to the other.
Since \( \vec{e} \) is along the x-axis and \( \vec{f} \) is along the y-axis, the angle between them is the angle between the x and y axes, which is \( 90^\circ \).
You can also confirm this by using the dot product formula: \( \vec{e} \cdot \vec{f} = |\vec{e}| |\vec{f}| \cos(\pi) \). Since the dot product is zero for perpendicular vectors, \( \cos(\pi) = 0 \), which implies \( \pi = 90^\circ \).
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