Respuesta :
the unit vector e which is collinear to vector a = (6,8) , and has the same direction is [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex] .
Step-by-step explanation:
Here we have , vector a = (6,8) . We need to find the unit vector e which is collinear to vector a = (6,8) , and has the same direction. Let's find out:
We know that for a vector [tex]a = (x,y)[/tex] the unit vector is given by :
⇒ [tex](\frac{x}{|a|} ,\frac{y}{|a|} )[/tex] , where |a| is modulus of vector a . So , Modulus of vector a is :
⇒ [tex]|a| = \sqrt{x^2+y^2}[/tex]
⇒ [tex]|a| = \sqrt{6^2+8^2}[/tex]
⇒ [tex]|a| = \sqrt{36+64}[/tex]
⇒ [tex]|a| = \sqrt{100}[/tex]
⇒ [tex]|a| =10[/tex]
Hence , unit vector is given by [tex](\frac{6}{10} ,\frac{8}{10})[/tex] or , [tex](\frac{3}{5} ,\frac{4}{5})[/tex] . Vector is already collinear as it's in same direction of original vector as :
⇒ [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex]
Therefore , the unit vector e which is collinear to vector a = (6,8) , and has the same direction is [tex]e=(\frac{3}{5} ,\frac{4}{5})[/tex] .
