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:

4

The vector equation for any line is

r(t)=point you want it to pass through+parameter⋅velocity vector.

You want it to pass through the point P=(−1,−5,2) and uses the parameter t, so we write

r(t)=(−1,−5,2)+t⋅velocity vector.

As it asked to set the velocity vector as the normal vector to the plane, and that is N=(1,−5,1), we get

r(t)=(−1,−5,2)+t(1,5,1).

The parameter could have been anything else. We could have chosen 2t,t/7 or 4t−3. What difference does it make?

In the first two cases we are changing the speed at which the point walks the line. With 2t it walks twice as faster, with t/7 it walks 1/7 slower.

The case (4t−3) changes both speed and at what time you pass through the desired point. With (4t−3) you'll pass through point P at the time t=3/4. Using the parameter t ensures that at time t=0, so to speak, you begin at point (−1,−5,2).

Answer 2

Step-by-step explanation:

find the vector equation of the line through the origin which is perpendicular to the plane

r.(i-2j+k)=3