Out of two vectors, the larger one is `sqrt(2)` times the smaller one . Show that the resultant cannot make an angle greater than `(pi)/(4)` with the larger one.

Explanation

Let the vectors be `sqrt(2) Q and Q ` and the resultant be R. Angle between R and `sqrt(2)Q` is `theta and angle ADB = alpha`
[Fig.2.15]

From `Delta ABD`,
`(AB)/(sinangleADB)=(BD)/(sinangleDAB) or, (sqrt(2)Q)/(sin alpha)=(Q)/(sin theta)`
`or, sin theta =1/(sqrt(2))=sin alpha`
`sinalphacancel(gt) 1,sin theta cancel(gt) 1/(sqrt(2))`
`"Hence", theta cancel(gt) (pi)/(4)`