Question

Maria works in a factory that produces new cars. She is having trouble with one of the machines. In order to work properly, the two gears in the machine must be perpendicular. Maria makes some adjustments and wants to know if the two gear shifts are aligned correctly. The new directional vectors of the gears are:g1= 5i -j+2k g2=I-3j-4k

Answer 1

Answer:

Maria did her job properly. Both gears are perpendicular.

Step-by-step explanation:

Recall that given vectors a and b, they are perpendicular if and only if $a\cdot b$ =0. If $a=(a_1,a_2),b=(b_1,b_2)$. Then $a\cdot b = a_1b1_+a_2b_2$.

IN our case a=(5,-1,2) and b) (1,-3,-4). So,

$a\cdot b = 5\cdot 1 + (-1)\cdot(-3) + 2\cdot(-4) = 5+3-8 =0$

So both gears are perpendicular.