Question

show that a=i^-j^÷√2 is the unit vector​

Answer 1

Answer:

$\vec{a}\:\text{is a unit vector}$

Explanation:

Show that $\vec{a}=\frac{\vec{i}}{\sqrt2}-\frac{\vec{j}}{\sqrt2}$ is the unit vector​

Unit vector:

A vector whose magnititude or length is one is called a unit vector

Given:

$\vec{a}=\frac{1}{\sqrt2}\vec{i}-\frac{1}{\sqrt2}\vec{j}$

Now,

$|\vec{a}|=\sqrt{(\frac{1}{\sqrt2})^2+(\frac{-1}{\sqrt2})^2}$

$|\vec{a}|=\sqrt{\frac{1}{2}+\frac{1}{2}}$

$|\vec{a}|=\sqrt{1}$

$|\vec{a}|=1$

$\implies\:\vec{a}\:\text{is a unit vector}$