Question

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

Answer 1

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

    $b = (1,1,5-2\sqrt{26} )$