Show that the points whose position vectors given by 
(i) \(-2\hat { i } +3\hat { j } +5,\hat { i } +2\hat { j } +3\hat { k } ,7\hat { i } -\hat { k } \) 
(ii) \(\hat { i } -2\hat { j } +3\hat { k } ,2\hat { i } +3\hat { j } -4\hat { k } \) and\(-7\vec { j } +10\vec { k } \)  are collinear.

The vertices of a triangle have position vectors \(4\hat { i } +5\hat { j } +6\hat { k } ,5\hat { i } +6\hat { j } +4\hat { k } ,6\hat { i } +4\hat { j } +5\hat { k } \) Prove that the triangle is equilateral.

Examine whether the vectors \(\hat { i } +3\hat { j } +\hat { k } ,2\hat { i } -\hat { j } -\hat { k } \) and  \(7\hat { j } +5\hat { k } \) are coplanar 

Show that the points whose positions vectors \(4\hat { i } -3\hat { j } +\hat { k } \) ,\(2\hat { i } -4\hat { j } +5\hat { k } \) ,\(\hat { i } -\hat { j } \) from a right angled triangle.

Find the vectors whose length 5 and which are perpendicular to the vectors \(\vec { a } =3\vec { i } +\vec { j } -4\vec { k } \) and \(\vec { b } =6\vec { i } +5\vec { j } -2\vec { k } \)