Given vectors $$ \mathbf{u} $$ and $$ \mathbf{v} $$ below, find $$ c $$ such that $$ \mathbf{u} $$ and $$ \mathbf{v} $$ are orthogonal. $$ \begin{aligned} \mathbf{u} & =[-5,2, c] \ \mathbf{v} & =[-3,3,-1] \ c & = ext { Ex: } 5\end{aligned} $$

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Given vectors $$ \mathbf{u} $$ and $$ \mathbf{v} $$ below, find $$ c $$ such that $$ \mathbf{u} $$ and $$ \mathbf{v} $$ are orthogonal. $$ \begin{aligned} \mathbf{u} & =[-5,2, c] \ \mathbf{v} & =[-3,3,-1] \ c & =	ext { Ex: } 5\end{aligned} $$

UpStudy AI · Accepted Answer

The vectors u = [-5, 2, c] and v = [-3, 3, -1] are orthogonal if their dot product is zero. The dot product is calculated as:

(-5)(-3) + (2)(3) + (c)(-1) = 15 + 6 - c = 21 - c

Setting the dot product equal to zero for orthogonality:

21 - c = 0

Solving for c:

c = 21

Thus, c = 21 makes the vectors orthogonal.
To make vectors **u** = [-5, 2, c] and **v** = [-3, 3, -1] orthogonal, set their dot product to zero: (-5)(-3) + (2)(3) + (c)(-1) = 0 15 + 6 - c = 0 c = 21 So, c = 21.

Given vectors \( \mathbf{u} \) and \( \mathbf{v} \) below, find \( c \) such that \( \mathbf{u} \) and \( \mathbf{v} \) are orthogonal. \( \begin{aligned} \mathbf{u} & =[-5,2, c] \\ \mathbf{v} & =[-3,3,-1] \\ c & =\text { Ex: } 5\end{aligned} \)

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