Determine whether the set of vectors is orthogonal.
-$$\left[ \begin{array} { l }
- 20 \
- 40 \
- 20
\end{array} \right] , \left[ \begin{array} { r }
20 \
0 \
- 20
\end{array} \right] , \left[ \begin{array} { l }
- 20 \
- 20 \
- 20
\end{array} \right]$$
A) $\mathrm { No }$
B) Yes

Question

Determine whether the set of vectors is orthogonal.
-$$\left[ \begin{array} { l } 
- 20 \
- 40 \
- 20
\end{array} \right] , \left[ \begin{array} { r } 
20 \
0 \
- 20
\end{array} \right] , \left[ \begin{array} { l } 
- 20 \
- 20 \
- 20
\end{array} \right]$$
A) $\mathrm { No }$
B) Yes

Quizplus · Accepted Answer

To determine if the set of vectors is orthogonal, we need to check if the dot product of each pair of vectors is zero. Calculating the dot products:1. For the first and second vectors: $(-20 \times 20) + (-40 \times 0) + (-20 \times -20) = -400 + 0 + 400 = 0$2. For the first and third vectors: $(-20 \times -20) + (-40 \times -20) + (-20 \times -20) = 400 + 800 + 400 = 1600$, which is not zero.3. We don't need to check the second and third vectors because we already found a pair that is not orthogonal.Since not all dot products are zero, the set of vectors is not orthogonal.

Determine Whether the Set of Vectors Is Orthogonal A) No\mathrm { No }No

Determine Whether the Set of Vectors Is Orthogonal A) $\mathrm { No }$