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1)

If A=3ˆi2ˆj+ˆk,B=ˆi3ˆJ+5ˆKand C=2ˆi+ˆj4ˆk forn a right angled triangle, then out of the following which one is satisfied ?


A) A=B+C and A2=B2+C2

B) A=B+C and B2=A2+C2

C) B=A+C and B2=A2+C2

D) B= A+C and A2=B2+C2

Answer:

Option B

Explanation:

Given,

 A=3ˆi2ˆj+ˆk,

B=ˆi3ˆJ+5ˆK

C=2ˆi+ˆj4ˆk

 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= (3ˆi2ˆj+ˆk).(2ˆi+ˆj4ˆk)

A.C= 6-2-4=0

 Hence, A and C  are perpendicular to each other 

Resultant of A and C  is B

1562021164_P3.PNG  B= A+C

 [according to triangle law]