Prove using vectors the mid-points of two opposite sides of a quadrilateral and the mid-points of the diagonals are the vertices of a parallelogram.

Find the unit vectors parallel to the sum of \(3\vec { i } -5\vec { j } +8\vec { k } \) and \(-2\vec { i } -2\vec { k } \) 

Prove that the points \(2\hat { i } +3\hat { j } +4\hat { k } ,3\hat { i } +4\hat { j } +2\hat { k } ,4\hat { i } +2\hat { j } +3\hat { k } \) form an equilateral triangle.

If \(\left| \vec { a } +\vec { b } \right| =60\),\(\left| \vec { a } -\vec { b } \right| =40;\) and \(\left| \vec { b } \right| =46\) find \(\left| \vec { a } \right| \)

Show that the vector \(\hat { i } +\hat { j } +\hat { k } \) is equally inclined with the coordinate axes.