Question

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).

Answer 1

(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