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

Options

A. `a+-b=0`
B. `a+-2b=0`
C. `2a+-b=0`
D. none of these

Answer

C

Explanation

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`