We read your photo as:

Given points A(1, 2, 0) and B(2, -1, 3), find the vector AB.

April 26, 2026Mathematics

ScanSolve AI Answer

Answer

\text{(c)} \hat{i} - 3\hat{j} + 3\hat{k}

4 steps

Identify the coordinates of points A and B.
Point A is $(1, 2, 0)$ .
Point B is $(2, -1, 3)$ .
Express the position vectors of points A and B.
The position vector of A is $\vec{OA} = 1\hat{i} + 2\hat{j} + 0\hat{k}$ .
The position vector of B is $\vec{OB} = 2\hat{i} - 1\hat{j} + 3\hat{k}$ .
Calculate the vector $\vec{AB}$ .
The vector $\vec{AB}$ is found by subtracting the position vector of A from the position vector of B:
$\vec{AB} = \vec{OB} - \vec{OA}$ $\vec{AB} = (2\hat{i} - \hat{j} + 3\hat{k}) - (\hat{i} + 2\hat{j} + 0\hat{k})$ $\vec{AB} = (2-1)\hat{i} + (-1-2)\hat{j} + (3-0)\hat{k}$ $\vec{AB} = 1\hat{i} - 3\hat{j} + 3\hat{k}$ $\vec{AB} = \hat{i} - 3\hat{j} + 3\hat{k}$
Compare the result with the given options.
The calculated vector $\vec{AB} = \hat{i} - 3\hat{j} + 3\hat{k}$ matches option (c).

The final answer is $\text{(c)} \hat{i} - 3\hat{j} + 3\hat{k}$ .