Find two vectors v1 and v2 whose sum is −4−5 , where v1 is parallel to 0−5 while v2 is perpendicular to 0−5

perpendicular
parallel

#1

Find two vectors v1 and v2 whose sum is −4−5 , where v1 is parallel to 0−5 while v2 is perpendicular to 0−5

Answer:

v1=r(0,-5) =>v1 is parallel to (0,-5)
v1+v2=(-4,-5)=> sum of v1 and v2
v2=(-4,-5)-r(4,-2)=> subtract v1
v2=(-4-4r,-5+2r)=> v2

v2•(0,-5)=0 => v2 is perpendicular to (0,-5)
(-4-4r,-5+2r)•(0,-5)=0 => we found v2 in the previous calculations
25-10r=0 => solve for r
10r=25
r=5/2

v1=r(0,-5)=(0,-25/2)=> find v1 by replacing r with 5/2
v2=(-4-4r,-5+2r)=(-14,0)=> find v2 by replacing r with 5/2

v1=r(0,-5)=(0,-25/2)
v2=(-4-4r,-5+2r)=(-14,0)