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Engineering Calculus Notes 67

# Engineering Calculus Notes 67 - 1.31 can be proved in two...

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1.4. PROJECTION OF VECTORS; DOT PRODUCTS 55 (c) −→ v = (1 , 0), −→ w = (3 , 2) (d) −→ v = (1 , 0), −→ w = (3 , 4) (e) −→ v = (1 , 2 , 3), −→ w = (3 , 2 , 1) (f) −→ v = (1 , 2 , 3), −→ w = (3 , 2 , 0) (g) −→ v = (1 , 2 , 3), −→ w = (3 , 0 , 1) (h) −→ v = (1 , 2 , 3), −→ w = (1 , 1 , 1) 2. A point travelling at the constant velocity −→ v = −→ ı + −→ + −→ k goes through the position (2 , 1 , 3); what is its closest distance to (3 , 1 , 2) over the whole of its path? Theory problems: 3. Prove Proposition 1.4.2 4. The following theorem (see Figure
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Unformatted text preview: 1.31 ) can be proved in two ways: Theorem 1.4.4. In any parallelogram, the sum of the squares of the diagonals equals the sum of the squares of the (four) sides. O Q P R −→ v −→ w Figure 1.31: Theorem 1.4.4 (a) Prove Theorem 1.4.4 using the Law of Cosines ( § 1.2 , Exercise 13 ). (b) Prove Theorem 1.4.4 using vectors, as follows:...
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