vector analysis help?

Question

Given the three points A(2,-3,1), B(-4,-2,6) and C(1,5,-3) can you please help me find the vector from A to the midpoint of the straight line joining B to C? Thanks!

let BC be the vector from B to C... then BC=5ax+7ay-9az... actually when finding the vector from B to C we don't add the vectors but we do Vector C -(minus) Vector B.....

Answer 1

To find midpt of BC add corrosponding co'ords and divide 'em by 2. so mid pt(P) is (-1.5,1,5,1.5)
To find a vector from A to P, subtract corrosponding co'ords.
-3.5i+4.5j+.5k

Answer 2

Hello,

you may first find the coordinates of the midpoint on the segment BC
So that midpoint has for coordinates
[ ( (-4 + 1,5)/2) ; ( (-2,6 + (-3) ) /2 ) ]

this is ( -5/4 ; -5,6/2 )

so the vector from a to this midpoint has the coordinates

( (-5/4 - 2) ; (-5,6/2 - 3,1) ) = ( - 3,25 ; -5,7 )

The vector is then -3,25 vectX -- 5,7 vectY

Answer 3

Let D be mid point of line joining B to C
D(-3/2 , 3/2 , 3/2)
Vector AD = d - a
Vector AD = (- 3/2 ** 3/2 ** 3/2) - (2 ** -3 ** 1)
Vector AD = (-7/2 ** 9/2 ** 1/2)