Question 48
If <span class="math-tex">\(\vec{a}\)</span> and <span class="math-tex">\(\vec{b}\)</span> are vectors such that <span class="math-tex">\(|\vec{a}|=13, |\vec{b}|=5\)</span> and <span class="math-tex">\(\vec{a}\cdot \vec{b}=60\)</span> then the value of <span class="math-tex">\(|\vec{a}\times \vec{b}|\)</span> is
📘 Step-by-Step Solution & Detailed Explanation:
Use \(|\vec{a} \times \vec{b}|^2 + (\vec{a} \cdot \vec{b})^2 = |\vec{a}|^2|\vec{b}|^2\):
\(|\vec{a} \times \vec{b}|^2 = 169 \times 25 - 60^2 = 4225 - 3600 = 625\)
\(|\vec{a} \times \vec{b}| = 25\)
Answer: (D) 25
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