What is the magnitude of the vector product from the vectors C = 1.5i + 6.2j and D = 4.4i + 7.3j?

To determine the magnitude of the vector product (also known as the cross product) of the two vectors C and D, we begin by noting that both vectors are in two dimensions. The cross product is defined in three dimensions, so when calculating the cross product of two 2D vectors, we can treat them as having a z-component of zero.

The vector C can be expressed as ( C = 1.5 \hat{i} + 6.2 \hat{j} + 0 \hat{k} ) and the vector D as ( D = 4.4 \hat{i} + 7.3 \hat{j} + 0 \hat{k} ).

The formula for the cross product ( C \times D ) is given by the determinant of the following matrix:

[

\begin{vmatrix}

\hat{i} & \hat{j} & \hat{k} \

1.5 & 6.2 & 0 \

4.4 & 7.3 & 0

\end{vmatrix}

]

Calculating this determinant, we focus on the ( \hat{k} ) component because the ( \hat{i} ) and