Two hikers in the mountains come to a fork in the trail. hiker \"A\" takes the l

Question

Two hikers in the mountains come to a fork in the trail. hiker "A" takes the left-hand fork while hiker "B" takes the right-hand one. An hour later A is 5 km north and 0.3 km down from the fork in the trail while B is 3 km south and 2 km east at the same altitude of the fork. Let i, j, and k be unit vectors pointing North, East, and Up, respectively.

1. The displacement of A from the fork is (all components in km)?____________(show all work and find the displacement and vector length)

2. the shortest distance from B to the fork in the trail is_________km?

3. the shortest distance from A to B is__________km?

Explanation / Answer

1) dA = (5i - 0j - 0.3 k) km <<<<<<<<<---------Answer

2) dB = (-3i + 2j + 0 k) km

|dB| = sqrt(3^2+2^2+0^2)

= 3.6 km <<<<<<<<<---------Answer

3)

dAB = sqrt((5-(-3))^2 + (-0-2)^2 + (-0.3-0)^2)

= 8.252 km <<<<<<<<<---------Answer

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