ANSWER
a) Orthogonal
b) Not orthogonal.
EXPLANATION
The given vectors are:
a)
[tex]v1 = \: < \: - 5,5 \: > [/tex]
and
[tex]v2= \: < \: 1,1 \: > [/tex]
If the dot product of two vectors is zero, then the two vectors are orthogonal.
[tex]v1 \bullet \: v2= - 5 \times 1 + 5 \times 1 [/tex]
[tex]v1 \bullet \: v2= - 5 \times 1 + 5 \times 1 = - 5 + 5[/tex]
[tex]v1 \bullet \: v2= 0[/tex]
These two vectors are orthogonal.
b)
The second pair of vectors are:
[tex]v1 = \: < \: 154, -169.4 \: > [/tex]
and
[tex]v2 = \: < \: 88,64 \: > [/tex]
[tex]v1 \bullet \: v2= 154\times 88 + - 169.4\times 64[/tex]
[tex]v1 \bullet \: v2= 13552 - 10841.6[/tex]
[tex]v1 \bullet \: v2= 2712.4[/tex]
This pair is not orthogonal.
