Question:
<p>Let \(\vec{a},\vec{b}\) be two non-zero non-collinear vectors. Then \(|\vec{a}\times\vec{b}|\) equals</p>
\(|\vec{a}||\vec{b}|\sin\theta\)
\(|\vec{a}||\vec{b}|\cos\theta\)
\(|\vec{a}||\vec{b}|\)
\(|\vec{a}||\vec{b}|\sin\theta\) with \(\vec{a}\times\vec{b}\perp\vec{a}\) and \(\vec{a}\times\vec{b}\perp\vec{b}\)
Step-by-Step Solution
Key Concept: Cross product magnitude is |a||b|sin\theta AND the result is perpendicular to both -- all of these properties together define the cross product.
By definition, \(\vec{a}\times\vec{b}\) is a vector with:
<ul>Magnitude \(|\vec{a}||\vec{b}|\sin\theta\)
Direction perpendicular to both \(\vec{a}\) and \(\vec{b}\)</ul>
Option D states both the magnitude formula AND the perpendicularity -- making it the most complete and correct statement. Answer: (D)
Correct Answer: D