A. VECTOR FORMS 1. Write vector ๐ดโ in its common/layman representation (NOTE: angle must be positive and between 0° and 180°) 2. 3. Write vector ๐ถโ in its polar form (NOTE: angle can be negative) 4. โโ in its navigation form Write vector ๐ท 5. Write vector ๐ธโโ in ๐ฬ-๐ฬ form โโ in its rectangular form Write vector ๐ต B. UNIT VECTORS, VECTOR ADDITION, & SCALAR-VECTOR MULTIPLICATION 1. Based on the same vectors illustrated above, find the unit vectors (expressed in ๐ฬ-๐ฬ form) of the following vectors: (HINT: solve for the operation on vector first, then proceed in finding the result’s unit vector & remember to do the multiplication first before addition) a. ๐ถโ b. โโ 2๐ท c. โโ ๐ดโ + ๐ต d. ๐ธโโ − ๐ถโ e. โโ + 3๐ท โโ ๐ต C. CONVERSION OF VECTOR FORMS & VECTOR MULTIPLICATION โโโ = ๐๐๐ ๐ต ๐๐° ๐พ, and ๐ฏ โโ = ๐๐ ๐๐° ๐๐๐ฌ๐ญ ๐จ๐ ๐๐จ๐ฎ๐ญ๐ก, ๐ฎ โโโโ = −๐๐ฬ − ๐๐๐ฬ : Given vectors ๐ญ 1. Find the vector ๐ผโ if ๐ผโ = ๐นโ ⋅ ๐บโ 2. Find the vector ๐ฝโ if โโ ๐ฝโ = ๐บโ × ๐ป 3. โโ if Find the vector ๐พ โโ = (๐นโ ⋅ ๐บโ ) ⋅ ๐ป โโ ๐พ 4. โโ if Find the vector ๐ฟ โโ = ๐ป โโ × (๐นโ ⋅ ๐บโ ) ๐ฟ D. WORD PROBLEMS EASY ROUND: Suppose Hadji lives in a subdivision where houses are arranged in a grid-like fashion. He wants to visit his longtime girlfriend Beau who had just recently moved into his subdivision. On the way to his girlfriend from his own house, as he was rolling through the street in a straight line due north, he noticed that he had passed 6 houses before turning 90° to the west, and had passed another 4 houses before arriving to her girlfriend’s house. Express the angle and distance between the two houses via a vector in navigation form. HARD ROUND: Andrea & Crystal the explorers find themselves lost in a dense jungle. They decide to use their trusty compass and map to navigate their way back to his camp. According to the map, the camp is located at a position represented by the vector ๐ถโ = (10, 5) in meters. However, the compass is malfunctioning and gives them incorrect directions. It tells them to walk in the direction of the vector โโโ = (3, 2) in meters. They unknowingly follow the compass's instructions and walk in that direction for a while. ๐ After some time, they realize their mistake and consult the map again. They determine that they have actually walked in the opposite direction of where they should have been going. Andrea & Crystal want to know how far they have deviated from the correct path. How far are they from the camp? To which direction (in common/layman form) should they face while walking in order to go back to camp?
