Answer:
Option B
Explanation:
Given,
A=3ˆi−2ˆj+ˆk,
B=ˆi−3ˆJ+5ˆK
C=2ˆi+ˆj−4ˆk
Here, |A|=√(3)2+(−2)2+(1)2
or |A|=√9+4+1=√14 .....(i)
|B|=√(1)2+(−3)2+(5)2
|B|=√1+9+25=√35 ......(ii)
and
|C|=√(2)2+(1)2+(−4)2
|C|=√4+1+16=√21 .........(iii)
From Eqs.(i) , (ii) and (iii) , we get
B2= A2+C2
(√35)2=(√14)2+(21)2
Now, A.C= (3ˆi−2ˆj+ˆk).(2ˆi+ˆj−4ˆk)
A.C= 6-2-4=0
Hence, A and C are perpendicular to each other
∴ Resultant of A and C is B
B= A+C
[according to triangle law]