1. Find two unit vectors that make an angle of 60* with v = <3,4>

2. Find the cross product a X b for a = i + (e^t)k +(e^-t)k, b = 2i + (e^t)j - (e^-t)k

3. Use the scalar triple product to determine whether the points A(1,3,2), B(3,-1,6),C(5,2,0), and D(3,6,-4) lie on the same plane.

1. ?

2. I set it up as the matrices way..

| i j k |

| 1 e^t e^-t |

| 2 e^t -e^-t |

and came out with -2i - (-e^-t - 2e^-t)j + (-e^-t-2e^t)k

3)

| 1 3 2 |

| 3 -1 6 |

| 5 2 0 |

|3 6 -4 |

is this the way to do this problem? I end up with like

|0|

|-4| if i do this.

can someone help me with these? I think i am doing 2 and 3 incorrectly and 1 i do not know how.

thanks.