Find a vector in the direction of vector (3\(\hat{i}\) + \(\hat{j}\)+2\(\hat{k}\)) which has magnitude 6 units

(6/√14){(3\(\hat{i}\) + \(\hat{j}\)+2\(\hat{k}\)) }

Let   vectors  \(\vec{a}\) = (3\(\hat{i}\) + \(\hat{j}\)+2\(\hat{k}\))     

    magnitude of (\(\vec{a}\)) =√(3)² +(1)² +(2)² = √14

   The unit vector in direction of   (\(\vec{a}\)) =  (\(\vec{a}\) )/|\(\vec{a}\)|

   So,  The unit vector in direction of  (\(\vec{a}\)) is a ̂ =(3i ̂ + j ̂+2k ̂) /√14

Hence, the unit vector in the direction of vector  (3\(\hat{i}\) + \(\hat{i}\)+2\(\hat{k}\)) which has magnitude 6 units is given by,

 6.\(\hat{a}\)  = 6.{(3\(\hat{i}\) + \(\hat{j}\)+2\(\hat{k}\)) /√14}

6.\(\hat{a}\)  = (6/√14){(3\(\hat{i}\) + \(\hat{j}\)+2\(\hat{k}\)) }