Question

Determine whether the given vectors are orthogonal, parallel, or neither. (a) a = 9, 6 , b = −4, 6

Answer 1

Answer:

Orthogonal

Step-by-step explanation:

We are given that a=<9,6>

b=<-4,6>

When two vectors are orthogonal then

$a\cdot b=0$

Using the formula

$<9,6>\cdot <-4,6>$

$-36+36=0$

Hence, vectors a and b are orthogonal.

When two vectors are parallel then

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

$\frac{a_1}{a_2}=\frac{9}{-4}=-\frac{9}{4}$

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

$\frac{a_1}{a_2}\neq \frac{b_1}{b_2}$

Hence, vectors are not parallel.