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The value of k, for which |k veca| lt |v...

The value of k, for which `|k veca| lt |veca|` and `kveca + 1/2 veca` is parallel to `veca` holds true are-

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If vecb ne 0 , then every vector veca can be written in a unique manner as the sum of a vector veca_(p) parallel to vecb and a vector veca_(q) perpendicular to vecb . If veca is parallel to vecb then veca_(q) =0 and veca_(q)=veca . The vector veca_(p) is called the projection of veca on vecb and is denoted by proj vecb(veca) . Since proj vecb(veca) is parallel to vecb , it is a scalar multiple of the vector in the direction of vecb i.e., proj vecb(veca)=lambdavecUvecb" " (vecUvecb=(vecb)/(|vecb|)) The scalar lambda is called the componennt of veca in the direction of vecb and is denoted by comp vecb(veca) . In fact proj vecb(veca)=(veca.vecUvecb)vecUvecb and comp vecb(veca)=veca.vecUvecb . If veca=-2hatj+hatj+hatk and vecb=4hati-3hatj+hatk and veca=vec_(p)+veca_(q) then veca_(q) is equal to

If vecb ne 0 , then every vector veca can be written in a unique manner as the sum of a vector veca_(p) parallel to vecb and a vector veca_(q) perpendicular to vecb . If veca is parallel to vecb then veca_(q) =0 and veca_(q)=veca . The vector veca_(p) is called the projection of veca on vecb and is denoted by proj vecb(veca) . Since proj vecb(veca) is parallel to vecb , it is a scalar multiple of the vector in the direction of vecb i.e., proj vecb(veca)=lambdavecUvecb" " (vecUvecb=(vecb)/(|vecb|)) The scalar lambda is called the componennt of veca in the direction of vecb and is denoted by comp vecb(veca) . In fact proj vecb(veca)=(veca.vecUvecb)vecUvecb and comp vecb(veca)=veca.vecUvecb . If veca=-2hatj+hatj+hatk and vecb=4hati-3hatj+hatk then proj vecb(veca) is