Answer :

Given Data:

Vectors:





Their Dot products are 0, 5 and 8.


Calculation:


Let the required vector be,



Now,




x + y -3z =0 …Eq. 1


Similarly




x + 3y - 2z = 5 …Eq. 2




2x + y + 4z = 8 …Eq. 3


Subtract Eq. 1 from Eq. 2


(x + 3y - 2z) – (x + y -3z) = 5 - 0


2y + z = 5 …Eq. 4


Subtract Eq. 3 from (2 × Eq. 2)


2(x + 3y - 2z) - 2x + y + 4z = (2 × 5) - 8


5y – 8z = 2 …Eq. 5


Adding Eq. 5 with (8 × Eq. 4)


8(2y + z) + (5y – 8z) = 8 × 5 + 2


21y = 42


y = 2


From Eq. 5,


5×2 - 8z = 2


z = 1


From Eq. 1


x + y -3z =0


x + 2 – 3×1 = 0


x = 1



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