Question

Determine if the pairs of vectors below are "parallel", "orthogonal", or "neither".

Answer 1

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,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

When vectors are orthogonal then,

$a_1a_2+b_1b_2+c_1c_2=0$

$\frac{a_1}{a_2}=\frac{-3}{-6}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{3}{6}=\frac{1}{2}$

$\frac{c_1}{c_2}=\frac{-5\times 5}{36}=-\frac{25}{36}$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}$

Hence, the vectors are not parallel.

$a_1a_2+b_1b_2+c_1c_2=-3(-6)+3(6)+(-5)(\frac{36}{5})=18+18-36=0$

Hence, the vectors are orthogonal.

b.a=(-3,3,-5), b=(-6,6,-10)

$\frac{a_1}{a_2}=\frac{-3}{-6}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{3}{6}=\frac{1}{2}$

$\frac{c_1}{c_2}=\frac{-5}{-10}=\frac{1}{2}$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}= \frac{c_1}{c_2}$

Hence, the vectors are parallel.

3.a=(-3,3,-5) and b=(12,-12,19)

$a_1a_2+b_1b_2+c_1c_2=-3(12)+3(-12)+(-5)(19)=-36-36-95\neq 0$

Hence, the vectors are not orthogonal.

$\frac{a_1}{a_2}=\frac{-3}{12}=-\frac{1}{4}$

$\frac{b_1}{b_2}=-\frac{3}{12}=-\frac{1}{4}$

$\frac{c_1}{c_2}=\frac{-5}{19}$

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}$

Hence, the vectors are not parallel.