Question

find the equation of the line through the point(3,2 1) and perpendicular to each the lines x+1÷2=y-1÷3=z+2÷-1,c-3÷2=y÷3=z-5÷4 is​

Answer 1

Answer:

Step-by-step explanation:

Equation of the line passing through (3,1,2) is  

a

x−3

​  

=  

b

y−1

​  

=  

c

z−2

​  

   -----   (1)

where a,b,c are the direction ratios of the line  

Since, the line is perpendicular to the given lines  

So,  

a+2b+3c=0  -----  (2)

3a+2b+5c=0  ----  (3)

Subtracting  (3) from (2), we get  

−2a−2c=0

a=−c

Putting a=−c in (2)

−c+2b+3c=0

b=−c

Putting a=−b and b=−c in equation (1)

−c

x−3

​  

=  

−c

y−1

​  

=  

c

z−2

​  

 

x−3=y−1=−(z−2)

x−3=y−1=2−z

Therefore,  

This the required equation of the line.