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Let vec(a)=6vec(i)-3vec(j)-6vec(k) and v...

Let `vec(a)=6vec(i)-3vec(j)-6vec(k) and vec(d)=vec(i)+vec(j)+vec(k)."Suppose that" vec(a)=vec(b)+vec(c) "where" vec(b) "is parallel to" vec(d) and vec(c) " si perpendicular to" vec(d). "Then" vec(c) "is-"`

A

`5vec(i)-4vec(j)-vec(k)`

B

`7vec(i)-2vec(j)-5vec(k)`

C

`4vec(i)-5vec(j)+vec(k)`

D

`3vec(i)+6vec(j)-9vec(k)`

Text Solution

Verified by Experts

The correct Answer is:
B
`vec(b)=lamda(hati+hat(j)+hat(k))`
`vec(a)=vec(b)+vec(c)`
`vec(c)=vec(a)-lamda (hati+hat(j)+hat(k))`
`vec(c)=(6hat(i)-3hatj-6hatk)-lamda(hati+hat(j)+hat(k))`
`vec(c)(6-lamda)hat(i)+(-3-lamda)hat(j)+(-6-lamda)hat(k)`
`vec(c).vec(lamda)=6-lamda-3-lamda-6-lamda=0`
`3lamda=3`
`lamda=-1`
`vec(c)=7hat(i)-2hat(j)-5hat(k)`
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