MTH 103 TMA AND ANSWER

1. if a=a force of 30N, acting in the east direction, b =a force of 40N, acting in the north direction. find the magnitude of the vector sum r of there forces.       ANSWER 50N

2.find the sum AB+BC+CD+DE+EF.   ANSWER   AF

3.find the sum BC+DC+DE+DE+EF.   ANSWER   BF

4.if Z1=3i+5j and Z2=7i+3j find the Z1-Z2.   ANSWER  -4I+2J.

5.if Z1=2i-4j and Z2=2i-6j and Z3=3i-j find the Z1-Z2-Z3.      ANSWER   -3i-9j

6.find the direction cosine [l,m,n] of the r=2i+4j-3k.    answer     2/root29, 4/root29, -3/root29

7.if a=2i+2j+k and b=3i+6j+2k,find the scalar product a and b   answer   6i-12j-2k

8.if a=5i+4j+2k, b=4i+5j+3k and c=2i-j-2k. determine value ab    answer   10i-4j-4k

9. if a=2i+4j+3k and b=i+5j-2k. find the vector product of a and b.    answer    -23i +7j+6k

10. a vector having direction opposite to that of vector A, both with the same magnitude is denoted by    answer    -A

11.find the distance between the point A(5,4) and B(7,6)          answer   2 root2

12.the gradient of the line A(4,3) and B(8,6)     answer   3/4

13.if a is (3,6) and b is (4,8). find the coordinate of the midpoint of ab     answer     (3 1/2, 7).

14. a straight line has a gradient of 5/3 and it passes through the point (1,3), find its equation      answer    5/3x - 8/3

15. find the angle between two lines -3x+4y=8 and -2x-8y-14=0    answer  -14.63

16. find the equation of the line through the point (-1,2) which is parallel to y=2x+1   answer y=3x+5

17. find the equation of the line through the point (-1,2) which is perpendicular to y=2x-1        answer -1/2x+3/2

18. if the slope of a line passing through the point A(3,2) is 3/4 . then find points on the line which are 5 units away from the point A.         ANSWER   (-1,2)

19 A dot  product is said to b distributive, if          answer     m(u.v)=v(m.v)

20 find the equation to the straight line passing through the point of intersection of the lines 5x-6y-1=0 and 3x+2y+5=0 and perpendicular to the line 3x-5y+11=0    answer       5x+3y +8=0

21.find the radius of the circle x^2+y^2+8x+6y=0    answer   5

22.find the center of the circle x^2+y^2+8x+6y=0    answer   (-4,-3)

23.given the equation of a circle is x^2+y^2+2x-6y=0. find the the center of the circle   answer   (-1,3).

24. given the equation of the circle is x^2+y^2+2x-6y-15. find the radius of circle     answer  5

25. find the point of the intersection of the intersection of the center x^2+y^2+3y=0 with line y=x-1   answer           (0,1) and (1,1)

26. find the parametric equations of a circle with center (2,-1) and radius 3        answer   x=2+3cos teta ,y=-1+3sin teta

27 find the center of a circle given by x=4+2cos teta, y=-3+2sin teta     answer    (4,-3)

28 find the vector product a *b if a=i+2j-k and b=2i+3j+k             answer      5i+3j-k

29 find the radius of a given circle x=4+2cos teta , y=-3+2sin teta         answer      2

30 find the equation of the circle with its center at the origin with point (-3,4) on the circle         answer  x^2+y^2=25

31find the directrix of the parabola whose equation is x^2+30y.        answer     -7 1/2

32find the focus ofthe parabola whose equation is y^2+32x              answer      f(-8,0)

33.find the focus in the equation y^2=5x           answer      f(1 1/4,0)

34.find the equation of the parabola having vertex (0,0) axis along the x-axis and pass through (2,-1)     answer       y^2=x/2

35.given that ellipse has an equation of 9x^2+4y^2=36     answer      x^2/2^2+y^2/3^2=36

36.given the equation 9x^2-16y^2=14, find the coordinate of the foci       answer f1(5,0) , f2(-5,0)

37.find the equation of th parabola with focus(-1,4) and directrix y=3       answer y=1/2x^2+x-4

38.find equation of an ellipse whose major axis is vertical, with the center location (-1,3) at the distance between the center and one of the convertices equal to 4, and the distance between the center and one of veritces equal to 6.      answer (x-1)^2/16 +(y-3)^2/36=1

39.find the asymptotes of the hyperbola whose equation given as  x^2/4-y^2/9=1          answer y=4/9x

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