‹ Back to the paper
Solve the following.
If A(1, 2, -3) and B(-1, -2, 1) are the end points of a vector A⃗B⃗ then find the unit vector in…
If $A(1, 2, -3)$ and $B(-1, -2, 1)$ are the end points of a vector $\vec{AB}$ then find the unit vector in the direction of $\vec{AB}$.
Answer
Answer
$\vec{AB} = (-1-1)\hat{i} + (-2-2)\hat{j} + (1+3)\hat{k} = -2\hat{i} - 4\hat{j} + 4\hat{k}$
$|\vec{AB}| = \sqrt{4+16+16} = 6$
Unit vector $= \frac{\vec{AB}}{|\vec{AB}|} = \frac{-2\hat{i} - 4\hat{j} + 4\hat{k}}{6}$
Hence the unit vector is $-\frac{1}{3}\hat{i} - \frac{2}{3}\hat{j} + \frac{2}{3}\hat{k}$.
Final answer: $-\frac{1}{3}\hat{i} - \frac{2}{3}\hat{j} + \frac{2}{3}\hat{k}$