This is Calculus and vector course and it's vector lesson for grade 12 high school.

Those are the questions I need help with. Total 6 questions with some small questions on it like a,b,c.

Part B 1. Consider two vectors a and b such that lal = 6, |b| = 10 , and the angle between them is 40. a. Find the magnitude of the vector a + b b. Find the angle between the vector a and the vector a + b c. Find the magnitude of the vector a - b 2. Find out if the points A(0,1,2), B(-1,1, -2), and C(-2, -3, -2) are collinear or not. 3. Consider the vectors a = 20[W] and b = 10 [$30.E]. a. Represent these vectors in a diagram. b. Find the magnitude and the direction of the vector sum a + b. 4. Consider a = 21 - 3j + 4k and b = -i+ 2j - k a. Represent the vector a using a 3D rectangular prism. b. Find a + b and a - b as algebraic vectors c. Find the magnitude of the vector -2a + 3b 5. Consider the triangle determined by the following points A(1,3,5), B(-2,0, -1), and C(4, -3,2). a. Find the coordinates of a point P such that OP = - _OA+OB+OC 3 b. Prove that PA + PB + PC = 0 6. Consider v = 1 + 2j - 3k a. Find the angles a, B, and y between the vector v and the coordinate axes. b. Show that cos a + cos B + cosy = 1