Consider the vector v = (-7,8). What is the angle between v = (-7,8) and the positive x-axis? Part 1: Use the formula v1 x v2=|v1||v2|cos theta to find the cosine of the angle between the two vectors (-7,8) and (1,0).

(1) To find the angle between v and positive x-axis, we first determine the angle formed by v and the negative x-axis. Since v = (-7,8), its vertical measure y is 8 units and horizontal measure x is 7 units.

arctan (8/7) = 48.81°

Solving for angle between v and positive x-axis:

180° - 48.81° = 131.19°

(2) v1 x v2=|v1||v2|cosθ

Calculating for the dot product of the vector:

v1 x v2 = - 7*1 + 8*0 = - 7

Calculating vector magnitude:

|v1| = √ (-7²+8²) = √113

|v2| = √ (1²+0²) = 1

cosθ = (v1 x v2) / |v1||v2| = - 7 / (√113 * 1) = - 0.659