Question

are the vectors orthogonal?\
\langle 3, 2\
angle, \langle -6, 18\
angle\
\bigcirc no\
\bigcirc yes

Explanation:

Step1: Recall the dot - product formula

For two vectors \(\vec{u}=(u_1,u_2)\) and \(\vec{v}=(v_1,v_2)\), the dot - product is \(\vec{u}\cdot\vec{v}=u_1v_1 + u_2v_2\).
Let \(\vec{u}=(3,2)\) and \(\vec{v}=(-6,18)\). Then \(\vec{u}\cdot\vec{v}=(3)\times(-6)+(2)\times(18)\).

Step2: Calculate the dot - product

$$
LATEXBLOCK0
$$

Since two non - zero vectors \(\vec{u}\) and \(\vec{v}\) are orthogonal if and only if \(\vec{u}\cdot\vec{v} = 0\). Here \(\vec{u}\cdot\vec{v}=18
eq0\).

Answer:

No