Answer:
1.Orthogonal
2.Parallel
3.Neither
Step-by-step explanation:
We have to find pair of vectors are parallel , orthogonal or neither.
1.a=(-3,3,-5) and b=(-6,6,36/5)
We know that when vectors are parallel then,
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]
When vectors are orthogonal then,
[tex]a_1a_2+b_1b_2+c_1c_2=0[/tex]
[tex]\frac{a_1}{a_2}=\frac{-3}{-6}=\frac{1}{2}[/tex]
[tex]\frac{b_1}{b_2}=\frac{3}{6}=\frac{1}{2}[/tex]
[tex]\frac{c_1}{c_2}=\frac{-5\times 5}{36}=-\frac{25}{36}[/tex]
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]
Hence, the vectors are not parallel.
[tex]a_1a_2+b_1b_2+c_1c_2=-3(-6)+3(6)+(-5)(\frac{36}{5})=18+18-36=0[/tex]
Hence, the vectors are orthogonal.
b.a=(-3,3,-5), b=(-6,6,-10)
[tex]\frac{a_1}{a_2}=\frac{-3}{-6}=\frac{1}{2}[/tex]
[tex]\frac{b_1}{b_2}=\frac{3}{6}=\frac{1}{2}[/tex]
[tex]\frac{c_1}{c_2}=\frac{-5}{-10}=\frac{1}{2}[/tex]
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}= \frac{c_1}{c_2}[/tex]
Hence, the vectors are parallel.
3.a=(-3,3,-5) and b=(12,-12,19)
[tex]a_1a_2+b_1b_2+c_1c_2=-3(12)+3(-12)+(-5)(19)=-36-36-95\neq 0[/tex]
Hence, the vectors are not orthogonal.
[tex]\frac{a_1}{a_2}=\frac{-3}{12}=-\frac{1}{4}[/tex]
[tex]\frac{b_1}{b_2}=-\frac{3}{12}=-\frac{1}{4}[/tex]
[tex]\frac{c_1}{c_2}=\frac{-5}{19}[/tex]
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]
Hence, the vectors are not parallel.
