position vector

Question

The position vector r of a particle P at time t is given by r=t^2i+(12-t)j. Find the value of t when:

(a) r is parallel to the vector i

(b) r is parallel to the vector i+j

Answer: (a) 12

(b) 3

I don't know how to calculate, help, please, thx!

Answer 1

最愛解答

(a) If vector r is parralle to vector i, there is no component in vector j,

i.e. 12-t = 0

t = 12

(b) If vector r is parallel to vector (i+j), i.e. the ratio of component of vector i to that of vector j is equal,

i.e. t^2/(12-t) = 1/1 = 1

t^2 = 12 - t

t^2 + t -12 = 0

(t+4)(t-3) = 0

t = 3 or -4

2007-10-28 19:40:17 補充：

t = -4 is rejected because time t >= 0Hence t = 3 only