Hello can you help me with this math question and this a homework assignment

Question

asked May 23, 2023 187k views

1 Answer

Amaal · Answer 1 · 2023-05-27T09:49:53+0000

We know that two vectors are ortogonal if and only if:

$\vec{v}\cdot\vec{w}=0$

where

$\vec{v}\cdot\vec{w}=v_1w_1+v_2w_2$

is the dot product between the vectors.

In this case we have the vectors:

$\begin{gathered} \vec{a}=\langle-4,-3\rangle \\ \vec{b}=\langle-1,k\rangle \end{gathered}$

the dot product between them is:

$\begin{gathered} \vec{a}\cdot\vec{b}=(-4)(-1)+(-3)(k) \\ =4-3k \end{gathered}$

and we want them to be ortogonal, so we equate the dot product to zero and solve the equation for k:

$\begin{gathered} 4-3k=0 \\ 4=3k \\ k=(4)/(3) \end{gathered}$

Therefore, for the two vector to be ortogonal k has to be 4/3.