Question 161537
Let {{{v=ai+bj}}}. Since ||v||=2, this means that {{{sqrt(a^2+b^2)=2}}}



Now let's compute {{{-4v}}}:



{{{v=ai+bj}}} Start with the given vector



{{{-4v=-4(ai+bj)}}} Multiply both sides by -4



{{{-4v=-4ai-4bj)}}} Distribute



So this means:


||-4v||={{{sqrt((-4a)^2+(-4b)^2)=sqrt(16a^2+16b^2)=sqrt(16(a^2+b^2))=sqrt(16)*sqrt(a^2+b^2)=4*sqrt(a^2+b^2)}}}=4||v||



So this shows us that the length of ||-4v|| is simply 4 times that of ||v||. So the length of ||-4v|| is 8 units



In other words, ||-4v||=8