Que.2 Do the following sums. (T/I) 1. Determine the value of k so that = [2 ,5] and = [k , 4] are perpendicular. 2. Write a scalar equation of a plane, given its parametric equations. 1 : x = 3 -2s +2t , Z = 5 - s -2t Y = 1 + 3s + t 3. Considertheplanes2x+6y-2z-5=0and5x+15y+kz-7=0 a. For what value of k are the planes parallel ? b. For what value of k are the planes perpendicular?

4. A tow truck is pulling a car from a ditch. The tension in the cable is 15 000 N at an angle of 40 to the horizontal. a) Draw a diagram showing the resolution of the force into its rectangular components b) Determine the magnitudes of the horizontal and vertical components of the force. 5. find b and c such that [-2 ,b,7] and [c ,6 ,21] are collinear. 5. if = [6 , 1 ,8] is orthogonal to = [k ,-4 ,5] determine the value(s) of k. 6. Show that the line [x ,y ,z] = [10, 5 ,16] + t[3,1 ,5] is contained in the plane x + 2y - z -4 =0

Que.3 Do the following sums.(C) 1. Describe the differences between airspeed , windspeed , and groundspeed when solving vector problems associated with airplane flight. 2. Which form of the equation of the planescalar, vector, or parametric would you use to find the x-, y-, and z-intercepts? Explain your reasons. 3. When algebraically determining the intersection of a plane and a line, the result is 0 = 0. What does this tell you about the plane and line? Justify your answer.

4. Explain what the term consistent means in the context of a system of three planes. 5. Find the point of intersection of lines l1 and l2. l1 : [x ,y ,z] = [7 ,2 ,-6] + s[2 ,1,-3] 6. Explain how the vectors , 5 , and -5 are related. 7. Draw a diagram resolving a 500-N force at 15 counterclockwise from the horizontal into its rectangular components. 8. What is the difference between [2,3] and (2,3) ?

9. Write some application of the dot product measure? 10. Describe the method you would use to plot the point (-3, 5,-7).