Answer
The length of $ v $ is $$\|v\|=\sqrt{26}\approx 5.1.$$ Also, we have $$2v+3(4i-k)=18i-2j+5k.$$
With length $\sqrt{353}\approx 18.8$
Work Step by Step
The length of $ v $ is given by $$\|v\|=\sqrt{9+1+16}=\sqrt{26}\approx 5.1.$$ Also, we have $$2v+3(4i-k)=6i-2j+8k+3(4i-k)=18i-2j+5k.$$
The length of this vector is:
$\sqrt{18^2+(-2)^2+5^2}=\sqrt{18^2+4+25}=\sqrt{353}\approx 18.8$
