Question

Find the vector equation of the line that passes through the point (1,5) and is parallel
to the line r =(3+7t) i + (1 - 3t)j.​

Answer 1

Answer:

The line passes through the point,

a

=2  

i

^

+3  

j

^

​  

+  

k

^

 

And parallel to the line,

b

=4  

i

^

−2  

j

^

​  

+3  

k

^

 

The vector equation of the line passing through a point and parallel to the given line is,

r

=  

a

+λ  

b

 

Substituting the values, we get,

r

=(2  

i

^

+3  

j

^

​  

+  

k

^

)+λ(4  

i

^

−2  

j

^

​  

+3  

k

^

)

r

=(2+4λ)  

i

^

+(3−2λ)  

j

^

​  

+(1+3λ)  

k

^

Step-by-step explanation: