Science:Math Exam Resources/Courses/MATH152/April 2016/Question A 06/Solution 1

To make the given two vectors ${\textbf {u}}$ and ${\textbf {v}}$ parallel, we need

$(*)\quad [1,1,a]={\textbf {u}}=c{\textbf {v}}=[c,2c,3c]$

for some non-zero $c$.

By comparing the first components, we have $c=1$.

However, from the second components, we get $2c=1$, so that $c={\frac {1}{2}}$.

Therefore, for any value of $a$, there is no non-zero constant $c$ to make $(*)$ hold.

In other words, there is no value of $a$ such that the given two vectors ${\textbf {u}}$ and ${\textbf {v}}$ are parallel.