ONLY FOR YEAR MODULEThis assignment covers chapter 2 & 3 of the prescribed book as well as the study guide, it is based on Study Units 2.1,2.2,2.3,3.1,3.2 & 3.3 of Chapters 2 & 3 of HCNote that this assignment will close on 29 August 2025 at 03:00 PMQuestion 1(1.1) Find an equation for the plane that passes through the origin (0,0,0) and is parallel to the plane -x+3y-2z=6.(1.2) Find the distance between the point (-1,-2,0) and the plane 3x-y+4z=-2.Question 2: 15 Marks(2.1) Find the angle between the two vectors vec(v)=(:-1,1,0,-1:)vec(v)=(:1,-1,3,-2:). Determine whether both vectors are perpendicular, parallel or neither.(2.2) Find the direction cosines and the direction angles for the vector vec(r)=(:0,-1,-2,34:).(2.3) HMW:Additional Exercises.Let vec(r)(t)=(:t,-1t,t2-2:). Evaluate the derivative of |)=1. Calculate the derivative of V(t)*vec(r)(t) whenever V(1)=(:-1,1,-2:) and V'(1)=(:1,-2,2:).(2.4) HMW:Additional Exercises.Assume that a wagon is pulled horizontally by an exercising force of 5 lb on the handle at an angle of 45 with the horizontal.(a) Illustrate the problem using a rough sketch.(b) Determine the amount of work done in moving the wagon 30 lb .(2.5) HMW:Additional Exercises.Let the vector vec(v)=(:3500,4250:) gives the number of units of two models of solar lamps fabricated by electronics company. Assume that the vector vec(a)=(:1008.00,699,99:) gives the prices (in Rand-ZA) of the two models of solar lamps, respectively.(a) Calculate the dot product of the two vectors vec(a) and vec(v).(b) Explain the meaning of the resulting answer you obtain in the question above.(c) Let assume that the price of original price of the solar lamps has decreased by 10%. Identify the vector operation used for this case.