Given vectors $$ \mathbf{u} $$ and $$ \mathbf{v} $$ below, find $$ a $$ such that $$ \mathbf{u} $$ and $$ \mathbf{v} $$ are orthogonal. $$ \begin{aligned} \mathbf{u} & =[-15,-5] \ \mathbf{v} & =[a,-12] \ a & = ext { Ex: } 5\end{aligned} $$

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Given vectors $$ \mathbf{u} $$ and $$ \mathbf{v} $$ below, find $$ a $$ such that $$ \mathbf{u} $$ and $$ \mathbf{v} $$ are orthogonal. $$ \begin{aligned} \mathbf{u} & =[-15,-5] \ \mathbf{v} & =[a,-12] \ a & =	ext { Ex: } 5\end{aligned} $$

UpStudy AI · Accepted Answer

Two vectors are orthogonal if their dot product equals 0. For vectors u = [–15, –5] and v = [a, –12], the dot product is:

(–15) * a + (–5) * (–12) = –15a + 60.

Setting the dot product equal to 0 gives:

–15a + 60 = 0.

Solving for a:

–15a = –60  
  a = 4.

Thus, the value of a is 4.
To make vectors **u** and **v** orthogonal, set their dot product to zero. Given **u** = [–15, –5] and **v** = [a, –12], the dot product is –15a + 60. Setting this equal to zero and solving for a gives a = 4.

Given vectors \( \mathbf{u} \) and \( \mathbf{v} \) below, find \( a \) such that \( \mathbf{u} \) and \( \mathbf{v} \) are orthogonal. \( \begin{aligned} \mathbf{u} & =[-15,-5] \\ \mathbf{v} & =[a,-12] \\ a & =\text { Ex: } 5\end{aligned} \)

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