Use the values of a and b below for Questions 1-3.

a = -2i + 4j

b = 3i – j

1. Find a unit vector with the same direction as a.
2. Find the dot product of a and b.
3. Find the cross product of a and b considered as 3-dimensional vectors.
4. Set your TI-89 to RADIAN mode and graph the vector-valued function

r(t) = (t· cost) i + (t· sint) j

on the t-interval [0, 4 ].

5. Switch to Degree Mode. A projectile is launched from the ground with an initial velocity of 210 ft/sec at an angle of 35° from the horizontal.

   1. Graph the path of the projectile using parametric equations and use the Trace feature to estimate the time when the projectile reaches its highest point.
   2. Find the estimated time when the projectile reaches its highest point analytically by finding when the vertical component of the corresponding velocity vector is zero.

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