Question

if one side of square be represented by vector 3î+4j+5k then the area of square is

Answer 1

Answer: let side of square is AB

So

vector of AB =3i+4j+5k

AB =| 3i+4j+5k |

AB =√(3)^2+(4)^2+(5)^2

AB= √9+16+25

AB=√50

side =√50

area of square =side*side

=√50*√50

=50

Step-by-step explanation:

Answer 2

Given:

Side of square=3i+4j+5k

To find:

Area of square

Solution:

Let side of square

$r=3i+4j+5k$

$\mid r\mid=\sqrt{x^2+y^2+z^2}$

Where r=$xi+yj+zk$

Using the formula

$x=\mid r\mid=\sqrt{3^2+4^2+5^2}=5\sqrt 2$ units

Area of square=$(Side)^2$

Using the formula

Area of square =$x^2=(5\sqrt 2)^2=50 square units$

Hence, the area of square=50 square units