Question

show that A bar=I cap - j cap upon root 2 is a unit vector​

Answer 1

Explanation:

Given that

$\bar{A}=\dfrac{1}{\sqrt 2}i-\dfrac{1}{\sqrt 2}j$

And we have to show that this is a unit vector

Unit vector

  vector which have have magnitude 1 unit.

Lets take a vector R

$\bar{R}=r_1i+r_2j$

If vector R is unite vector then it magnitude(|R|) should be 1.

$|R|=\sqrt{r_1^2+r_2^2}$

Now by taking the magnitude of vector A

$|A|=\sqrt{\left (\dfrac{1}{\sqrt 2} \right )^2+\left (\dfrac{1}{\sqrt 2} \right )^2}$

So |A|=1

It means that vector A is a unit vector.