Thread: Find vector whose tail and head are....

Find the vector, V, whose tail and head are the midpoint of AB and the midpoint of BC, respectively:

A = (-8, 4, 1)
B = (3, 6, 8)
C = (7, 5, 6)

AB = <3 + 8, 6 - 4, 8 - 1> = <11, 2, 7>
BC = <7 -3, 5 - 6, 6 - 8> = <4, -1, -2>

MidPoint of AB = 1/2AB = <11/2 , 1 , 7/2>
MidPoint of BC = 1/2BC = <2, -1/2, -1>

Vector R from MidPoint of AB to MidPoint of BC = <2 - 11/2 , -1/2 - 1, -1 - 7/2>
== <-7/2, -3/2, -9/2>

But this is not correct. Where have I gone wrong? Hopefully I've made a simple error and not overlooked a fundamental concept. Thanks!

Originally Posted by blackbear

Find the vector, V, whose tail and head are the midpoint of AB and the midpoint of BC, respectively:

A = (-8, 4, 1)
B = (3, 6, 8)
C = (7, 5, 6)

AB = <3 + 8, 6 - 4, 8 - 1> = <11, 2, 7>
BC = <7 -3, 5 - 6, 6 - 8> = <4, -1, -2>

MidPoint of AB = 1/2AB = <11/2 , 1 , 7/2> nope! mid point of AB is {PV(A)+PV(B)}/2... where PV means position vector.
MidPoint of BC = 1/2BC = <2, -1/2, -1> same mistake.

Vector R from MidPoint of AB to MidPoint of BC = <2 - 11/2 , -1/2 - 1, -1 - 7/2>
== <-7/2, -3/2, -9/2>

But this is not correct. Where have I gone wrong? Hopefully I've made a simple error and not overlooked a fundamental concept. Thanks!

did this help?