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Finger [1]
2 years ago
6

If a =5, 0, −1,find a vector b such that compab = 2.b = _______.

Mathematics
1 answer:
Arturiano [62]2 years ago
7 0

Answer:

b  =  (q,r , 5q-2\sqrt{26} )

Step-by-step explanation:

From the question we are told that

The vector given is  

               a = (5,0,-1)

  Also  comp_a b =  2

Generally

       comp_a b  =  \frac{a \cdot b}{|a|}

Here  |a| is the magnitude of  a which is mathematically represented as

      |a| =  \sqrt{5^2  + 0^2  +(-1)^2 }

=>     |a| =  \sqrt{26}

b is vector which we will assume to have the following parameters

     b  =  (q , r , x)

So

        comp_a b =  \frac{(5,0,-1) \cdot (q,r,x)}{\sqrt{26} } =  2

=>     \frac{5q + 0 -x}{\sqrt{26} } = 2

=>     x =  5q-2\sqrt{26}

Hence the vector be can be mathematically represented as

      b  =  (q,r , 5q-2\sqrt{26} )

This means that the vector b is more than one value  since it is made up of variable

This means that if

   q = 1\\r=1\\x =1

Then

    b  =  (1,1,5-2\sqrt{26} )

         

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