1. Two vectors a and b are placed tail to tail and have magnitudes 4 and 6 respectively. There is an angle of 105 degree between the vectors. What is a . b?
2. Let u, v, and w be three mutually perpendicular vectors of lengths 2, 3, and 4, respectively. What is the value of (u - v + w) . (u + v - w) ?
3. Given the vectors a = (3, 4, 3) and b = (-1, 2, 4). What is the angle between vectors a and b?
4. What is the value of k ? Given two vectors a = (-1, 2, -3), b = (-6k, -1, k) and angle between them is 90 degree.