Question

Find the unit vector of vector A - B. Where vector A = 2i - j + 2k unit and B = -i -2j +2k unit

Answer 1

Answer:

3i+j

Explanation:

Answer 2

Answer:

$\dfrac{3\hat i+\hat j}{\sqrt{10}}$

Explanation:

Given:

• $\vec A = 2\hat i-\hat j+2\hat k$

• $\vec B = -\hat i-2\hat j+2\hat k$

$\vec A-\vec B = ( 2\hat i-\hat j+2\hat k)-(-\hat i-2\hat j+2\hat k) \\=(2-(-1))\hat i+(-1-(-2))\hat j+(2-2)\hat k\\=3\hat i+\hat j+0\hat k$

The magnitude of $\vec A-\vec B$ is given by

$|\vec A-\vec B| = \sqrt{3^2+1^2+0^2} = \sqrt{10}$

Thus, unit vector of $\vec A-\vec B$ is given by

$\hat n = \dfrac{\vec A-\vec B}{|\vec A -\vec B|}=\dfrac{3\hat i+\hat j+0\hat k}{\sqrt{10}}=\dfrac{3\hat i+\hat j}{\sqrt{10}}$