 By Ertuðrul Tarhan

ISBN-10: 9752661521

ISBN-13: 9789752661523

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Extra resources for Vectors in the Plane (Zambak).

Sample text

Find the value of a if u = (a, 1) is perpendicular to v = (3, 4). 2. In the right triangle ABC, AC is the hypotenuse, BH ⊥ AC, and H lies on AC. −→ −→ −→ −→ Find (HC + CB)⋅(AB + BH). → 3. Find an equation for the line passing through P(3, –1) which is perpendicular to n = (3, 1). Answers 4 1. a = − 3 2. 0 C. COMPONENT OF 3. 3x + y – 8 = 0 → → u ALONG v (OPTIONAL) → → The scalar component of u along v (or the scalar → → component of u in the direction of v) is given by → → | u|⋅cos θ, where θ is the angle measure between u and → v.

Find | a + b|. → 1. | a| = 3, | b| = 5, and the angle between a and A) 7 B) 8 C) 9 D) 10 E) 11 6. In the right triangle ABC, m∠A = 90°, D ∈ [AC], −→ −→ and |AB| = k. Find BA ⋅ BD. A) k B) k2 C) k2 2 D) k 2 E) 2k2 → 7. What is the angle between a = (1, ñ3) and |AB| = |AC| = 4, 120° m∠A = 120°, and 2 A) 60° 2 C) 30 C) 135° 8. A square ABCD has side C B B) 36 B) 120° D) 150° E) 180° D 4 |AD| = |DC|. −→ −→ Find BC ⋅ BD. A) 48 → b = (–4, –4ñ3) in degrees? A 2. In the figure, D) 24 E) 18 K A B P 3 cm, and K, L are the midpoints of sides AB and Q L BC respectively.

Using the Sketchad we can move H to find the shortest possible time in the problem. We can use computer applications such as The Geometer’s Sketchpad, Cabri Geometry, or Javascript sketchpad to sketch vectors and solve problems. We can use an application to a problem, and then change certain values to see their effect. We can also use a computer application to add and subtract vectors, and to multiply a vector by a scalar. EXERCISES Project: y Use The Geometer’s Sketchpad, Cabri Geometry, or Javascript sketchpad to sketch the vectors → →→ →→ → 2 u, – v, u + v, u – 3⋅ v and −→ −→ PQ, QP if P(3, –4) and Q(4, –3).