a (non-zero) vector perpendicular to both ⎛⎝⎜−1−50⎞⎠⎟(−1−50) and ⎛⎝⎜−4−13⎞⎠⎟(−4−13) is

Question

A (non-zero) vector perpendicular to both

$\begin{pmatrix}-1\\-5\\0\end{pmatrix}$ and $\begin{pmatrix}-4\\-1\\3\end{pmatrix}$ is

🧐 Not the exact question you are looking for?Go ask a question

Solution

To find a vector that is perpendicular to both given vectors, we can use the cross product. The cross product of two vectors gives a vector that is perpendicular to both of the original vectors.

The given vectors are: Vector A = (-1, -5, 0) Vector B = (-4, -1, 3)

The cross product of A and B is calculated as follows:

The cross product, C = A x B, is given by:

Cx = AyBz - AzBy = (-53) - (0-1) = -15 Cy = AzBx - AxBz = (0*-4) - (-13) = 3 Cz = AxBy - AyBx = (-1-1) - (-5*-4) = 1 - 20 = -19

So, the vector that is perpendicular to both A and B is C = (-15, 3, -19).

This problem has been solved

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.

a (non-zero) vector perpendicular to both ⎛⎝⎜−1−50⎞⎠⎟(−1−50) and ⎛⎝⎜−4−13⎞⎠⎟(−4−13) is

Question