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)

Answer 1

suppose v1=(a1, a2, a3) and v2=(b1, b2, b3)
a1 + b1= 3
a2 + b2= 0
a3 + b3=2

a1 = -4k
a2= -2k
a3= -4k

and -4 b1- 2b2 - 4b3=0

Answer 2

a1+a2+a3+b1+b2+b3=5
(-4k-2k-4k) + (b1+b2+b3)=5
b1+b2+b3=5 +10k

and -4 b1- 2b2 - 4b3=0

Answer 3

so b2=10+20k
a2 + b2= 0
so k=-5/9
now solve by your own..

Answer 4

how did you get b2=10+20k...and thanks so much

Answer 5

b1+b2+b3=5 +10k

and -4 b1- 2b2 - 4b3=0
multiply 1st equation by 4 and add to 2nd equation...