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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 + 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 =