Show that v = a1+ bj is perpendicular to the line ax + by-c by establishing that

ID: 2889957 • Letter: S

Question

Show that v = a1+ bj is perpendicular to the line ax + by-c by establishing that the slope of the vector v is the negative reciprocal of the slope of the given line. Determine the slope of the vector v= ai + bj The slope of the vector is Determine the slope of the line ax + by=c. The slope of the line is What is the relationship between the two slopes obtained in the previous steps. Select the correct choice below. O A. The slope of the vector is the reciprocal of the slope of the line. O B. The slope of the vector is the negative of the slope of the line. C. O D. The slope of the vector is equal to the slope of the line. The slope of the vector is the negative reciprocal of the slope of the line. This shows that the vector v = ai + bj is | to the line ax + by = c.

Explanation / Answer

Given vector v=ai+bj

therfore slope of vector v=tan(theta)=j component / i component = b/a ....................(1)

Now given line is ax+by=c

=> by=-ax+c

=> y= -ax/b + c/b = mx +C where m is slope of line

so slope of line = -a/b ...............................(2)

from equation (1) and (2) it is clear that

slope of the vector is the negative reciprocal of the slope of the line (D)

and this show vector v=ai+bj is perpendicular to the line ax+by=c

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Show that v = a1+ bj is perpendicular to the line ax + by-c by establishing that

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