Let a = 2i - 3j + 4k and b = 7i + j - 6k. If r * a = r * b, r ⋅ (i + 2j + k) = -3, then r ⋅ (2i - 3j + k) is equal to:

If a,b are any two perpendicular vectors of equal magnitude and |3a+4b| + |4a-3b| = 20, then |a| equals: ____________

If the sides AB, BC and CA of triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to:
<!-- [if !supportLineBreakNewLine]-->
<!--[endif]-->

Let the position vectors of points 'A' and 'B' be i+j+k and 2i+j+3k, respectively. A point 'P' divides the line segment AB internally in the ratio λ:1(λ>0). If O is the origin and OB.OP - 3|OA×OP|² = 6, then λ is equal to