Question

find the vector equation of the line through the origin which is perpendicular to the plane
r.(i-2j+k)=3​

Answer 1

Answer:

Step-by-step explanation:

n general, the normal vector of the plane a⋅x+b⋅y+c⋅z+d=0 is (a,b,c).

Hence, the normal vector of the plane 1⋅x−5⋅y+1⋅z−1=0 is (1,−5,1).

Hence, the line can be represented by t as

x−(−1)1=y−(−5)−5=z−21=t.

Thus,

r(t)=(t−1,−5t−5,t+2).