Que.1 [A] Do the following multiple choice questions. 1. A line in two-space has scalar equation 3+ 5y + 9 = 0. Which vector is parallel to the line? a. [3,5] b. [3.-5] c. [5,3] d. [-5,3] 2. Which plane does not contain the point P(10, -3, 5)? a. 3x+6y-2z-2=0 b. X+y-z-12=0 c. 2x-2y-3z-11=0 d. 4x+5y+z-30=0 3. How many solutions does this system have? 10x -7y = 10 4x + 5y = 12 a. 0 b. 1 c. 12 d. Infinitely many Que.1[B] do the following sums : 1.Usethefollowingsetofvectorstodrawadiagram of ??? +?-??.

3.Convert each true bearing to its equivalent quadrant bearing. g. 130 h. 080 4. Write a force of 200 N at 20to the horizontal in Cartesian form. ??????? 5. Find the coordinates and magnitude of vector?? ,for A(1 ,3) and B(7,2). 6. Calculate the dot product for the followings. a. ??? = [2 ,4] ??? = [3 ,-1] b.???=2i+3j ??? =9i-7j 7. calculate the angle between the vectors ??? = [7 ,8] and ??? = [4 ,3] 8. determine the projection of ??? and ??? if I??? I = 56 , I??? I = 100 ,angle between ??? and ??? is 125.

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

3.Convert each true bearing to its equivalent quadrant bearing. g. 130h. 0804. Write a force of 200 N at 20to the horizontal in Cartesian form.???????5. Find the coordinates and magnitude of vector?? ,for A(1 ,3) and B(7,2).6. Calculate the dot product for the followings. a. ??? = [2 ,4] ??? = [3 ,-1]b.???=2i+3j ??? =9i-7j7. calculate the angle between the vectors ??? = [7 ,8] and ??? = [4 ,3]8. determine the projection of ??? and ??? if I??? I = 56 , I??? I = 100 ,angle between ??? and ??? is 125.

Que.1[B] do the following sums : 1. Use the following set of vectors to draw a diagram of a + b- c. 2.In hexagon ABCDEF, opposite sides are parallel and equal, FC =2AB . Let AB = u and FA = v A B D Express the following vector in terms of u and v e. CF f. FDQue.1 [A] Do the following multiple choice questions. 1. A line in two-space has scalar equation 3+ 5y + 9 = 0. Which vector is parallel to the line? a. [3,5] b. [3.-5] c. [5,3] d. [-5,3] 2. Which plane does not contain the point P(10, -3, 5)? a. 3x + 6y-2z -2 =0 b. X+y-z-12 =0 c. 2x -2y -3z -11 = 0 d. 4x + 5y +z -30 = 0 3. How many solutions does this system have? 10x -7y = 10 4x + 5y = 12 b. 1 c. 12 d. Infinitely many Que.1[B] do the following sums : 1.Use the following set of vectors to draw a diagram of a + b - c. 2.In hexagon ABCDEF, opposite sides are parallel and equal, FC =2AB . Let AB = u and FA = v D