Physics (vector) Question

Question

Dear experts,

Im having an issue understanding the following Physics question...

The vector product between two vectors of known intensity is maximum when:

1) the scalar product between the same vectors is zero

2) the scalar product between the same vectors is minimal

3) the vectors are parallel and have the same direction

4) the vectors are parallel and have opposite directions

5) the vectors have the same modulus

The answer is 1, i still don't understand why it's the answer, my 1st thought was about number 3

(I have no idea what a scalar product is and internet search didn't help me a lot understanding it)

Answer 1

The other tutor's answer is absolutely correct, so let me address your question about scalar products. A scalar product (dot product) is the result of multiplying two vectors together that do not produce a vector product (cross product).

For example, work (not a vector) is the product of force (a vector) times displacement (also a vector). The equation for work is, W = Fdcosθ, where θ is the angle between the direction of the force vector, and the direction of the displacement vector. If F and d are parallel, and in the same direction, then θ=0° and the work done is a maximum, but if F and d are perpendicular, then θ=90°, and the work done is a minimum (zero).

Answer 2

Vector product magnitude is ABsin(θ_AB) and the dot product magnitude is ABcos(θ_AB). The maximum for vector product is when the angle between the vectors is 90° or perpendicular. This corresponds to the minimum of magnitude for the dot product of 0.

Please consider a tutor. Take care.