Engineering Calculus Notes 102

# Engineering Calculus Notes 102 - 90 CHAPTER 1 COORDINATES...

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Unformatted text preview: 90 CHAPTER 1. COORDINATES AND VECTORS 1. Calculate each determinant below: (a) 1 −2 34 (b) −1 2 3 −4 (c) −1 2 4 −8 2. Sketch the triangle △ABC and indicate its orientation; ﬁnd σ (A, B, C )A (△ABC ): (a) A(0, 0), B (2, 1), C (1, 2) (b) A(1, 2), B (2, 0), C (3, 3) (c) A(2, 1), B (1, 3), C (3, 2) →→ 3. Calculate − × − : v w → (a) − = (1, 2, 3), v → − = (3, 1, 2), (b) v →→ (c) − = − , v ı →→ (d) − = − , v ı → − = (3, 1, 2) w → − = (6, 5, 4) w →→ − =− w → − → −=k w → −→ → − → → → → → (e) − = 4− − 3− + 7 k , − = −2− − 5− + 4 k v ı w ı 4. Find the oriented area vector A (△ABC ) and calculate the area of the triangle: (a) A = (0, 0, 0), B = (1, 2, 3), C = (3, 2, 1) (b) A = (1, 3, 2), B = (2, 3, 1), C = (3, 3, 2) (c) A = (2, −1, −4), B = (−1, 1, 0), C = (3, −3, −2) Theory problems: ...
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