SOLUTION: Given that: u = 6i−2j−8k and v = −7j−2k q1) Find a vector in the same direction as u but equal in magnitude to v? q2) Find a vector in the same di

Algebra ->  Points-lines-and-rays -> SOLUTION: Given that: u = 6i−2j−8k and v = −7j−2k q1) Find a vector in the same direction as u but equal in magnitude to v? q2) Find a vector in the same di      Log On


   

Question 852131: Given that: u = 6i−2j−8k and v = −7j−2k
q1) Find a vector in the same direction as u but equal in magnitude to v?
q2) Find a vector in the same direction as v but with a magnitude of 4?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1) Find the magnitude of v first.
abs%28v%29=sqrt%28%28-7%29%5E2%2B%28-2%29%5E2%29=sqrt%2853%29
Find the "u" unit vector by dividing it by its magnitude.
abs%28u%29=sqrt%286%5E2%2B%28-2%29%5E2%2B%28-8%29%5E2%29=sqrt%28104%29=+2%2Asqrt%2826%29
So the u unit vector would be
(6+%2F%282%2Asqrt%2826%29%29 ,-2%2F%282%2Asqrt%2826%29%29,-8%2F%282%2Asqrt%2826%29%29)
So then multiply the u unit vector by the magnitude of v.
(%286%2Asqrt%2853%29%29+%2F%282%2Asqrt%2826%29%29 ,%28-2%2Asqrt%2853%29%29%2F%282%2Asqrt%2826%29%29,%28-8%2Asqrt%2853%29%29%2F%282%2Asqrt%2826%29%29)
(3%2Asqrt%2853%2F26%29 ,-sqrt%2853%2F26%29,-4%2Asqrt%2853%2F26%29%29)
.
.
2) The v unit vector is
(0.0 ,-7%2Fsqrt%2853%29,-2%2Fsqrt%2853%29)
Just multiply this by 4,
(0.0 ,-28%2Fsqrt%2853%29,-8%2Fsqrt%2853%29)
(0.0 ,-%2828%2F53%29%2Asqrt%2853%29,-%282%2F53%29%2Asqrt%2853%29)