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If the vector vecb is collinear with the...

If the vector `vecb` is collinear with the vector `vec a =( 2sqrt2,-1,4) `and `|vecb| =10`, then

A

`a+-b=0`

B

`a+-2b=0`

C

`2a+-b=0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
It is given that b is collinear with the vector a.
`thereforeb=lamda a` . . . (i)
`=2sqrt(2)lamda hati-lamda hatj+4lamda hatk`
also, `|b|=10`
`implies sqrt((2sqrt(2))^(2)+(-lamda)^(2)+(4lamda)^(2))=10`
`implies 25lamda^(2)=100`
`implies lamda=+-2` . .(ii)
From eqs. (i) and (ii), we have
`b=+-2a, implies 2a+b=0`
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