Question

Given two vectors A⃗ = 4.20 i^+ 7.00 j^ and B⃗ = 5.70 i^− 2.60 j^ , find the scalar product of the two vectors A⃗ and B⃗ .

Answer 1

Applying the concept of scalar product. We know that vectors must be multiplied in their respective corresponding component and then add the magnitude of said multiplications. That is, those corresponding to the $\hat {i}$ component are multiplied with each other, then those corresponding to the $\hat {j}$ component and so on. Finally said product is added.

The scalar product between the two vectors would be:

$\vec{A} \cdot \vec{B} = (4.2\hat{i}+7\hat{j})\cdot (5.7\hat{i}-2.6\hat{j})$

$\vec{A} \cdot \vec{B} = (4.2*5.7) +(7*(-2.6))$

$\vec{A} \cdot \vec{B} = 5.74$

Therefore the scalar product between this two vectors is 5.74