Question

Find the vector product pq of the two vectors shown beow

Answer 1

The vector product of the two vectors is (-3, -6, 11).

To find the vector product of
`$\mathbf{p}$` and
`$\mathbf{q}$`, we can use the following formula:

`$\mathbf{p} * \mathbf{q} = \begin{vmatrix} \hat{\imath} & \hat{\jmath} & \hat{k} \\ \\ p_x & p_y & p_z \\ \\ q_x & q_y & q_z \end{vmatrix}$`

where
`$\hat{\imath}$`,
`$\hat{\jmath}$`, and
`$\hat{k}$` are the unit vectors in the x, y, and z directions, respectively.

Substituting the components of
`$\mathbf{p}$` and
`$\mathbf{q}$` into the formula, we get:

`$\mathbf{p} * \mathbf{q} = \begin{vmatrix} \hat{\imath} & \hat{\jmath} & \hat{k} \\ \\ 1 & 2 & 3 \\ \\ 4 & 5 & 6 \end{vmatrix}$`

Expanding the determinant, we get:

`$\mathbf{p} * \mathbf{q} = -3 \hat{\imath} - 6 \hat{\jmath} + 11 \hat{k}$`

Therefore, the vector product of
`$\mathbf{p}$` and
`$\mathbf{q}$` is (-3, -6, 11).

Question:

Find the vector product of the two vectors
`$\bold{p}$` and
`$\bold{q}$` shown below.

Vectors:

`$\bold{p} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$`

`$\bold{q} = \begin{pmatrix} 4 \\ 5 \\ 6 \end{pmatrix}$`