A class XII student appearing for a competitive examination was asked to attempt the following questions.Let  \(\vec a,\vec b\) and \(\vec c\) be three non zero vectors.1. If  \(\vec a\) and  \(\vec b\) are such that \(|\vec a+\vec b|=|\vec a-\vec b|\) thena. \(\vec a\perp\vec b\)b. \(\vec a||\vec b\) c. \(\vec a=\vec b\)d. None of these2. If \(\vec a=\hat i-2\hat j,\) \(\vec b=2\hat i+\hat j+3\hat k\) then evaluate \((2\vec a+\vec b).[(2\vec a+\vec b)\times(\vec a-2\vec b)]\)a. 0b. 4c. 3d. 23. If  \(\vec a\) and  \(\vec b\)are unit vectors and θ be the angle between them then \(|\vec a-\vec b|\) isa. \(sin\cfrac{\theta}2\)b. 2 \(sin\cfrac{\theta}2\)c. 2 \(cos\cfrac{\theta}2\)d. \(cos\cfrac{\theta}2\)4. Let \(\vec a,\,\vec b\) and  \(\vec c\) be unit vectors such that \(\vec a.\vec b=\vec a.\vec c=0\) and angle between \(\vec b\) and  \(\vec c\) is \(\cfrac{\pi}6\) then \(\vec a\) =a. 2(\(\vec b\times\vec c\)). b. -2(\(\vec b\times\vec c\)) c. ±2(\(\vec b\times\vec c\)) d. 2(\(\vec b\pm\vec c\))5. The area of the parallelogram formed by \(\vec a\) and \(\vec b\) as diagonals isa. 70b. 35c. \(\cfrac{\sqrt{70}}2\)d. \(\sqrt{70}\)