- Verify
d
dt
(f×g)=
df
dt
×g+f×
dg
dt
for the two vectors:
f=ti− 2 t^2 j+etkg=costi− 2 tj
11.14 Reinforcement
1.The free vectorsa,b,care shown as arrows in the figure below. Sketch arrows
representing the vectors
(i) a+b (ii) a−c (iii) a+ 2 b (iv)
1
2
(a+b) (v)
3
2
a−b (vi) a− 2 c
a
c b
2.Determine the unknown vectorxin terms ofa,b,cin each case.
(i) 3x−a+ 2 b= 2 a− 4 b−x
(ii) 2x− 2 a+ 3 c= 3 c− 2 b− 2 x
(iii) 4x− 3 a+ 2 b−c= 4 b− 2 x− 3 a+ 2 c
3.Write down the coordinates of the six points which lie on the coordinate axes and are
one unit from the origin.
4.Plot on a diagram the positions of
(0, 0, 2); (0,−1, 0); (3, 0, 0); (1, 1, 0); (−2, 1, 0)
(2, 0, 1); (0, 1, 1); (1, 1, 1); (−2, 1,−1); (1,−2, 2)
5.Calculate the distance from the origin of each of the points:
(i) (1, 1, 0) (ii) (2, 0,−1) (iii) (−2, 0, 1) (iv) (−2, 3, 1)
(v) (0, 4, 3) (vi) (
√
2, 1, 1)
6.Find the distance between each of the following pairs of points:
(i) (2, 0, 0); (1, 2, 3) (ii) (3, 0,−1); (1, 2, 1)
(iii) (5, 4, 2); (0, 3,−1) (iv) (−2,−1, 1); (0, 2,−2)
(v) (a,−a,0);(−a,0,a)
