I’ve studied vectors but I can’t do this question in a book.
PQRS is a rhombus of side 4 units. K, L, M and N are the mid-points of PQ, QR, RS and SP, respectively. SN® is a representative of vector u and SM® a representative of vector v. Show that SK®.SL® = 5u.v + 16.
The rhombus has P at the top left corner and S directly below. Q is slightly lower than P and R is directly below Q.
I think you're confusing with . When you take the dot product of a vector with itself, the angle is 0, so you just get the square of the length of the vector. But when the vectors are different, as in , that no longer applies. That is why the answer to the question leaves as it is, without attempting to evaluate it. Unless you know the angle of the rhombus, you can't evaluate .