please answer all parts of the attached question **Problem 8: Vector Length and Perpendicularity**Find a vector of length:**a.** 10 units which is perpendicular to \(\begin{pmatrix} 3 \\ -4 \end{pmatrix}\)**b.** \(3\sqrt{2}\) units which is perpendicular to \(\begin{pmatrix} 1 \\ -1 \end{pmatrix}\)**c.** \(\sqrt{20}\) units which is perpendicular to \(\begin{pmatrix} -2 \\ -1 \end{pmatrix}\)In this problem, you are tasked with finding vectors with specified lengths that are perpendicular to given vectors. Perpendicular vectors, or orthogonal vectors, have a dot product of zero. The dot product of two vectors \(\begin{pmatrix} a \\ b \end{pmatrix}\) and \(\begin{pmatrix} c \\ d \end{pmatrix}\) is defined as:\[ a \cdot c + b \cdot d = 0 \]When asked to find a perpendicular vector of a certain length, you must determine a vector that holds this property and also has the specified magnitude (length).

Name: please answer all parts of the attached question **Problem 8: Vector L
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: please answer all parts of the attached question **Problem 8: Vector Length and Perpendicularity**Find a vector of length:**a.** 10 units which is perpendicular to \(\begin{pmatrix} 3 \\ -4 \end{pmatrix}\)**b.** \(3\sqrt{2}\) units which is perpendic