SOLUTION: If // v // = 2, what is //-4v//?

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Question 161537: If // v // = 2, what is //-4v//?
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Let v=ai%2Bbj. Since ||v||=2, this means that sqrt%28a%5E2%2Bb%5E2%29=2


Now let's compute -4v:


v=ai%2Bbj Start with the given vector


-4v=-4%28ai%2Bbj%29 Multiply both sides by -4


-4v=-4ai-4bj%29 Distribute


So this means:

||-4v||=sqrt%28%28-4a%29%5E2%2B%28-4b%29%5E2%29=sqrt%2816a%5E2%2B16b%5E2%29=sqrt%2816%28a%5E2%2Bb%5E2%29%29=sqrt%2816%29%2Asqrt%28a%5E2%2Bb%5E2%29=4%2Asqrt%28a%5E2%2Bb%5E2%29=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