Problem

Given two points A (1, 2, 3) and B (4, -1, 5), find the position vector of B in respect to A.

Answer

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Answer

Subtracting A→ from B→, we get BA→=B→−A→=⟨4,−1,5⟩−⟨1,2,3⟩=⟨4−1,−1−2,5−3⟩=⟨3,−3,2⟩.

Steps

Step 1 ：The position vector of B in respect to A, denoted as BA→, is given by B→−A→.

Step 2 ：First, we find the position vectors of A and B. The position vector of a point P(x,y,z) is given by OP→=⟨x,y,z⟩, where O is the origin (0, 0, 0). Therefore, A→=⟨1,2,3⟩ and B→=⟨4,−1,5⟩.

Step 3 ：Subtracting A→ from B→, we get BA→=B→−A→=⟨4,−1,5⟩−⟨1,2,3⟩=⟨4−1,−1−2,5−3⟩=⟨3,−3,2⟩.

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