1. (a) Determine if vector \(\vec{w} = (-6, 13, -8)\) is coplanar with the plane spanned by vectors \(\vec{u} = (3, -1, 5)\) and \(\vec{v} = (4, -5, 6)\). Show all your steps and write a concluding sentence.
(b) Draw a sketch of the vectors and their relationship as determined in part (a) above (no numerical scale need be shown, but show axes, and label vector names and coordinates).
OR
2. On a soccer field, the sideline is oriented in a North-South direction. The goalie Gina stands in the middle of the northern goal crease on the goal line, from which she kicks the ball 25m into the field at an angle of W35°S. Her teammate Louisa takes this pass and kicks it a further 40m parallel to the sideline (ie. due south). Include a diagram:
(a) Define the overall resultant displacement vector of the ball after these two kicks. Express direction in terms of bearing. (b) If the field is 110m long, how far must the next striker kick the ball to take a shot at the center of the other team's goal, and in what direction (expressed as bearing).
