## 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

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1 week 2022-01-11T14:59:01+00:00 1 Answer 0 views 0

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 + bj

x 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 =