Did you know?
Did you know that vectors can be used to represent quantities with both magnitude and direction? In the given text, vectors A⃗ and B⃗ are represented in the form of i^ and j^, where i^ represents the unit vector in the x-direction and j^ represents the unit vector in the y-direction.
One interesting fact is that vector C⃗ lies in the xy-plane, meaning that it has no component in the z-direction. This implies that vector C⃗ is parallel to the ground and doesn't have any vertical component.
Another fascinating aspect is that vector C⃗ is perpendicular to vector A⃗. This means that if we were to draw these vectors, they would meet at a right angle. One possible visual representation is A⃗ pointing towards the right and C⃗ pointing straight up.
Lastly, the scalar product (also known as dot product) of vector C⃗ with B⃗ is given to be 15.0. The scalar product is a mathematical operation that results in a scalar quantity. It measures the projection of one vector onto another. In this case, it tells us that the projection of vector C⃗ onto vector B⃗ has a magnitude of 15.0. This can be visualized as one vector casting a shadow onto another.
