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
