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The compenent of vec(A)=hat(i)+hat(j)+5h...

The compenent of `vec(A)=hat(i)+hat(j)+5hat(j)` perpendicular to `vec(B)=3hat(i)+4hat(j)` is

A

`-(4)/(25)hat(i)+(3)/(25)hat(j)+5hat(k)`

B

`-(8)/(25)hat(i)-(6)/(25)hat(j)+5hat(k)`

C

`(4)/(25)hat(i)-(3)/(25)hat(j)+5hat(k)`

D

`+(8)/(25)hat(i)-(6)/(25)hat(j)+5hat(k)`

Text Solution

Verified by Experts

The correct Answer is:
C

`vec(A)_(11)=Acostheta=A((vec(A).vec(B))/(AB))=(vec(A).vec(B))/(A)=(3+4)/(5)=(7)/(5)`
`vec(A)_(11)=(7)/(5)((3hat(i)+4hat(j))/(5))=(7)/(25)(3hat(i)+4hat(j))`
`vec(A)_(11)=(21)/(25)hat(i)+(28)/(25)hat(j)`
`vec(A)_(bot)=(hat(i)+hat(j)+5hat(k))-((21)/(25)hat(i)+(28)/(25)hat(j))`
`(4)/(25)hat(i)-(3)/(25)hat(j)+5hat(k)`
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