Given vectors A = 6i + 3j and B = i + 9j, what is their scalar product AxB?

To find the scalar product (also known as the dot product) of two vectors, you multiply their corresponding components and then sum those products. Given vectors A = 6i + 3j and B = i + 9j, you can break it down as follows:

1. Identify the components of each vector:

• Vector A has a component of 6 in the i direction and 3 in the j direction.

• Vector B has a component of 1 in the i direction and 9 in the j direction.

2. Calculate the dot product using the formula:

( A \cdot B = (A_x \cdot B_x) + (A_y \cdot B_y) )

3. Substitute the components into the formula:

• The i components multiply to give: ( 6 \cdot 1 = 6 )

• The j components multiply to give: ( 3 \cdot 9 = 27 )

4. Add the results together:

( A \cdot B = 6 + 27 = 33 )

Therefore, the scalar product of the vectors A and B is 33, making that the correct answer. This calculation aligns