Question

Show that a vector is equal to i cap subtract j cap divided by root 2 is a unit vector.​

Answer 1

Explanation:

As per the question,

We know that , the vector having a magnitude of one is called unit vector.

Now,

According to given vector of the question,

$a = \frac{i-j}{\sqrt{2} }$

Magnitude of a vector a=xi + yj is written in mathematical form is:

$|a| = \sqrt{x^{2}+y^{2}$

Therefore magnitude of given vector,

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

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

|a| = 1

Therefore the given vector is unit vector.

Hence, proved.