## a. Show that the vector v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of v is the negative reciprocal

Question

a. Show that the vector v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of v is the negative reciprocal of the slope of the given line.

b. Determine the slope of the vector : v = ai + bj

in progress
0

Math
1 week
2022-01-11T14:59:01+00:00
2022-01-11T14:59:01+00:00 1 Answer
0 views
0
## Answers ( )

Answer:Part A:Hence proved that Vector= ai + bj is perpendicular to the line ax + by = c.Part B:Slope of vector =Step-by-step explanation:Condition for perpendicular is:

Part A:Consider the vector v = ai + bjx component of vector=a

y component of vector=b

Slope of vector=Consider the line ax + by = c:Rearranging the equation:ax+by=c

by=c-ax

y=According to general equation of line:Where m is the slope

In our case the slope of above line is:

According to the condition of perpendicular:

Hence proved that Vector= ai + bj is perpendicular to the line ax + by = c.Part B:Slope of vector is also calculated above.Since the slope of vector is negative reciprocal of the slope of the given line:

According to equation of line ax + by = c

y=According to general equation of line:Where m is the slope

Slope of given line=m=

negative reciprocal of the slope of the given line =

Slope of vector =