If the position vectors of points T and S are 3a, - 2a, +a, and 4a, + 6a, + 2a, respectively, find (a) the coordinates of T and S, (b) the distance vector from T to S, (c) the distance between T and S.

Hayley Bernard 2022-07-30 Answered
If the position vectors of points T and S are 3a, - 2a, +a, and 4a, + 6a, + 2a, respectively, find (a) the coordinates of T and S, (b) the distance vector from T to S, (c) the distance between T and S.
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Answers (1)

gutsy8v
Answered 2022-07-31 Author has 14 answers
Taking the coordinate system with A X , A Y , A Z as unit vectors in 3 noncoplanar directions,.
a. the coordinates of t and s are
t is [3,-2,1] and s is [4,6,2]
b.distance vector from t to s is s t = [ 4 3 , 6 + 2 , 2 1 ] = [ 1 , 8 , 1 ] = A X + 8 A Y + A Z
c.distance from t to s = [ ( A X + 8 A Y + A Z ) . ( A X + 8 A Y + A Z ) ]
If A X , A Y , A Z are mutually orthogonal unit vectors then we get
distance from t to s = 1 + 64 + 1 = 66
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