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

User Ayla
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1 Answer

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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)) .

User Govindpatel
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