Trigonometry Vectors

Question

1. Find the magnitude and direction of U=(0,-1) where theta is greater than or equal to 0 and less than 2pi.
2. Lets find V=(9,9)  Find a vector U that is half the length of V and points in the same direction as V.
3. A woman leaves home and walks 2 miles west, then 5 miles southwest. How far from home is she, and in what direction must she walk to head directly home? Round to the nearest tenth.

Answer 1

1. U=(0,-1) U = 0i - 1j = -j

2.V=(9,9) U=(4.5,4.5) = 4.5i +4.5j

3.walks 2 miles west, = -2i

walks 5 miles SW = -2.5√2i -2.5√2j

= -(2+2.5√2)i - 2.5j

= -5.536i - 2.5j

She must walk 5.5i +2.5j to get back home.