Question

Find the unit vector e which is collinear to vector a = (6,8) , and has the same direction.

Answer 1

the unit vector e which is collinear to vector a = (6,8) , and has the same direction is
`e=((3)/(5) ,(4)/(5))` .

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
`a = (x,y)` the unit vector is given by :

⇒
`((x)/(|a|) ,(y)/(|a|) )` , where |a| is modulus of vector a . So , Modulus of vector a is :

⇒
`|a| = √(x^2+y^2)`

⇒
`|a| = √(6^2+8^2)`

⇒
`|a| = √(36+64)`

⇒
`|a| = √(100)`

⇒
`|a| =10`

Hence , unit vector is given by
`((6)/(10) ,(8)/(10))` or ,
`((3)/(5) ,(4)/(5))` . Vector is already collinear as it's in same direction of original vector as :

⇒
`e=((3)/(5) ,(4)/(5))`

Therefore , the unit vector e which is collinear to vector a = (6,8) , and has the same direction is
`e=((3)/(5) ,(4)/(5))` .