Please complete number 57 and explain step by step, thankyou.
Use Theorem 2 to explain why the dot product v w does not change if both v and w are rotated by the same angle theta. Sketch the vectors e1 = 1, 0 and e2 = and determine the vectors obtained by rotating e1, e2 through an angle pi/4. Verify that e1 e2 = e'1 e'2. Determine ||v + w|| if v and w are unit vectors separated by an angle of 30 degree. What is the angle between v and w if: v w = - ||v|| ||w|| v w = 1/2 ||v|| ||w|| 59. Suppose that ||v|| = 2 and ||w|| = 3, and the angle between v and w is 120 degree. Determine:
Show transcribed image textUse Theorem 2 to explain why the dot product v w does not change if both v and w are rotated by the same angle theta. Sketch the vectors e1 = 1, 0 and e2 = and determine the vectors obtained by rotating e1, e2 through an angle pi/4. Verify that e1 e2 = e'1 e'2. Determine ||v + w|| if v and w are unit vectors separated by an angle of 30 degree. What is the angle between v and w if: v w = - ||v|| ||w|| v w = 1/2 ||v|| ||w|| 59. Suppose that ||v|| = 2 and ||w|| = 3, and the angle between v and w is 120 degree. Determine: