Question

Three drone cameras A, B and C are recording a hockey match. Their positions with respect to a control tower are given by the following coordinates:

A(1, 4, 6), B(3, 4, 5) and C(5, 4, 4).

Using vector method, show that the drone cameras A, B and C are moving in a straight path while recording the match.

Answer 1

Based on the coordinates A(1, 4, 6), B(3, 4, 5) and C(5, 4, 4).

`vec(AB) = (3 − 1)hati + (4 − 4)hatj + (5 − 6)hatk = 2hati + 0hatj − hatk`

`vec(AC) = (5 − 1)hati + (4 − 4)hatj + (4 − 6)hatk = 4hati + 0hatj − 2hatk`

The image uses the ratio of direction ratios:

`a_1/a_2 = 2/4 = 1/2`,

`b_1/b_2 = 0/0`

`c_1/c_2 = (−1)/(−2) = 1/2`