Question

are the vectors orthogonal?
\\( \langle 3, - 9 \
angle, \langle - 6, - 2 \
angle \\)
no
yes

Explanation:

Step1: Recall the dot - product formula

For two vectors \(\vec{u}=\langle a,b
angle\) and \(\vec{v}=\langle c,d
angle\), the dot - product is \(\vec{u}\cdot\vec{v}=ac + bd\).
Let \(\vec{u}=\langle3,-9
angle\) and \(\vec{v}=\langle - 6,-2
angle\). Then \(a = 3\), \(b=-9\), \(c=-6\), \(d = - 2\).

Step2: Calculate the dot - product

$$
LATEXBLOCK0
$$

Step3: Use the orthogonality condition

Two non - zero vectors \(\vec{u}\) and \(\vec{v}\) are orthogonal if and only if \(\vec{u}\cdot\vec{v}=0\).

Answer:

Yes