Introduction of Vector

The projection of the vector \[\hat{i} + \hat{j} + \hat{k}\] along the vector of \[\hat{j}\] is

The vector component of \[\vec{b}\] perpendicular to \[\vec{a}\] is 

If \[\vec{a} \text{ and } \vec{b}\] are two unit vectors inclined at an angle θ, such that \[\left| \vec{a} + \vec{b} \right| < 1,\] then 

If \[\vec{a} \text{ and } \vec{b}\] are unit vectors, then which of the following values of \[\vec{a} . \vec{b}\] is not possible? 

If \[\left| \vec{a} \right| = \left| \vec{b} \right|, \text{ then } \left( \vec{a} + \vec{b} \right) \cdot \left( \vec{a} - \vec{b} \right) =\]

Let \[\vec{a} , \vec{b} , \vec{c}\] be three unit vectors, such that \[\left| \vec{a} + \vec{b} + \vec{c} \right|\] =1 and \[\vec{a}\] is perpendicular to \[\vec{b}\]  If \[\vec{c}\] makes angles α and β with \[\vec{a} and \vec{b}\] respectively, then cos α + cos β =

The orthogonal projection of \[\vec{a} \text{ on } \vec{b}\] is 

If θ is an acute angle and the vector (sin θ) \[\text{i}\]  + (cos θ) \[\hat{j}\]  is perpendicular to the vector \[\hat{i} - \sqrt{3} \hat{j} ,\] then θ =