Question 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 v =1,1,0,1v =1,1,3,2. Determine (3) whether both vectors are perpendicular, parallel or neither. (2.2) Find the direction cosines and the direction angles for the vector r =0,1,2,34.(2.3) HMW:Additional Exercises. Let r(t)=t,1 t , t 22. Evaluate the derivative of r(t)|t=1. Calculate the derivative of V(t)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 v =3500,4250 gives the number of units of two models of solar lamps fabricated by electronics company. Assume that the vector 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 a and 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. 40 MAT1503/101/0/2026(2.6) HMW: The force exerted on a rope pulling a toy wagon is 30 N. The rope is 30 above the horizontal. (a) Illustrate the problem by means of a sketch (b) Determine the force that pulls the wagon over the ground. (2.7) Let v =1,3,5.(4)(a) Show that the set of all unit vectors in R 3 orthogonal to v lies on a circle. (b) Determine the center, radius, and a parametric description of this circle. (2.8) Let u =3,2k,k, and v =2,(4)52,k.(a) Find all real values of k for which u is orthogonal to v.(b) For those k, determine whether the vector u +v is also orthogonal to u v.(2.9) Let a =x, y, z be a unit vector in R (4)3 such that it is orthogonal to both u =2,1,1 and v =1,2,2.(a) Show that a must be parallel to u v.(b) Find the unit vector a satisfying the above conditions