Question

Please help fast... ​

Answer 1

Answer:

$a = \frac{i - j}{ \sqrt{2} } \\ \\ |a| = \frac{ |i - j| }{ \sqrt{2} } = \frac{ \sqrt{2} }{ \sqrt{2} } = 1 \\ \\ It's\: \: magnitude \: \: is \: \: one \: \: so \: \: it \: \: is\: \: a \: \: unit \: \: vector.$

Answer 2

\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}