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 = 