Find two vectors v1 and v2 and whose sum is(3,0,2) , where v1 is parallel to(-4,-2,-4) while v2 is perpendicular to (-4,-2,-4)

Question

Find two vectors v1 and v2   and  whose sum is(3,0,2) , where v1  is parallel to(-4,-2,-4)  while v2 is perpendicular to (-4,-2,-4)

amistre64 · Answer

since v1 is parallel to .... then it is in fact equal to any scalar of .....

amistre64 · Answer

and since v2 is perp to v1 by default; we need to pull a vector out of the plane that v1 is normaled to

amistre64 · Answer

at any case:

-4,  -2   ,  -4
-4a, -2b, -4c
-------------
-4-4a = 3

-2-2b = 0

-4-4d = 2

would be equations to fit in

amistre64 · Answer

as well as 16a + 4b + 16c = 0 for the dot