f) Let \( \underline{v} \) be a vector in 3-dimensional space. Prove that \( \underline{v} \cdot \underline{v}=1 \) if and only if \( |\underline{v}|=1 \).

3.4.1 What type is triangle \( A B C \) ?

4] (a) If the points \( A(1,4), B(-1,-2) \) and \( C(2,-3) \) are vertices atriangle, prove that.. \( \triangle A B C \) is right angled at \( B \), and find its area

9. In the given figure \( D L \) and \( B M \) are the heights corresponding to sides \( A B \) and \( A D \) respectively of parallelogram \( A B C D \). If the area of parallelogram is \( 300 \mathrm{~cm}^{2}, A B=30 \mathrm{~cm} \) and \( A D=20 \mathrm{~cm} \). Find the length of \( B M \) and \( D L \).

14. Find the radius of a hemisphere of volume \( 80 \mathrm{~cm}^{3} \)

An equilateral triangle it's perimeter equals 27 cm , then it's side length is......