1. The problem statement, all variables and given/known data Find two vectors, v1, and v2, whose sum is <-4,1,1>, where v1 is parallel to <2,5,-4>, and where v2 is perpendicular to <2,5,-4> 2. Relevant equations I am guessing I use the cross product for this equation, but I'm confused about how to start this problem. 3. The attempt at a solution any hlep at all would be greatly appreciated!
Don't use the cross product. Write v1 and v2 using coordinates. You're given that they add to <-4, 1, 1>. You're also given that v1 is parallel to <2, 5, -4>, which means that v1 is some constant multiple of <2, 5, -4>. You're also given that v2 is perpendicular to <2, 5, -4>. Two vectors being perpendicular should suggest a particular operation.
So, first I realized that v1= K<2,5,-4> Then I figured that since v1+v2=sum, ; then: <4,1,1> - K<2,5,-4> = v2 Now, what process would I use to find K?
Then what are the coordinates of v1? How about finding coordinates for v2 first? Also what can you do with the given information that v2 is perpendicular to <2, 5, -4>?