Check whether the following statements are true or false. Justify your answer with a short explanation or a counter example 

(i) The numbers  are the direction cosines of a line. 

(ii) The points  and  are collinear. 

(iii) The conic  is degenerate

(iv) Intersection of the ellipsoid  and the plan  is a circle. The conicoid  is non-central.  

(vi) The line

(i) False. The direction cosines of a line must satisfy the condition that the sum of the squares of the direction cosines equals 1. However, for the given numbers \(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{3}},\frac{3}{2}\), the sum of the squares of these values is not equal to ___ ______ ___ ___ __________ ___ ____.
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