2 Find the quantty u v uv assuming uaJvi4 3 pts 3 Express th

2. Find the quantty u v) (u-v) assuming u-a+Jv-i-4 (3 pts) 3. Express the vector with initial point P and terminal point Q in component form. Pr-8,-5), Q(-3, -3) (2 pts) Find the magnitude and direction (in degrees) of the vector. If necessary round your answer to two decimal places. (2 pts) 4. (a) |y| = (b) 5. A river flows due south at 5 mi/h. A swimmer attempting to cross the river heads due east swimming at 3 mih relative to the water. Find the true velocity of the swimmer as a vector. (3 pts) 3 mi/h s mih

Solution

2) u = 2i + j

     v = i – 4j

      u + v = 3i – 3j

       u – v = i + 5j

     (u + v).(u - v) = 3(i - j).(i + 5j) = 3*(1 - 5) = -12

3) P(-8, -5)   Q(-3, -3)

     v = (-3 + 8)I + (-3 + 5)j

     v = 5i + 2j

4) v = i + j

(a) |v| = sqrt(1^2 + 1^2) = sqrt(2)

(b) Theta = arctan(1/1) = 45 degree