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In the isosceles triangle ABC, |vec(AB)...

In the isosceles triangle `ABC, |vec(AB)| = |vec(BC)| = 8`,a point E divide AB internally in the ratio `1:3`, then the cosine of the angle between `vec(CE)` and `vec(CA)` is (where `|vec(CA)| = 12`)

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To solve the problem step by step, we will use vector properties and the cosine formula. Here’s the detailed solution: ### Step 1: Set Up the Triangle Given the isosceles triangle \( ABC \) where \( | \vec{AB} | = | \vec{BC} | = 8 \) and \( | \vec{CA} | = 12 \). We can place the points in a coordinate system for easier calculations. Let: - \( A = (0, 0) \) - \( B = (8, 0) \) - \( C = (4, h) \) where \( h \) is the height of the triangle from point \( C \) to the base \( AB \). ...
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