Answer:
The nonzero vector orthogonal to the plane is <-9,-8,2>.
Step-by-step explanation:
Consider the given points are P=(0,0,1), Q=(−2,3,4), R=(−2,2,0).
The nonzero vector orthogonal to the plane through the points P,Q, and R is
Expand along row 1.
Therefore, the nonzero vector orthogonal to the plane is <-9,-8,2>.
To find the equation of the line, we need to figure out the slope and y-intercept.
To find the y-intercept, look at the number where the line intersects the y-axis. The number is 5. The equation so far is y = ?x + 5.
We still didn't figure out the slope yet. To figure out the slope, pick two points. Use the rise over run method. It is in the image below. The line is going up to the left, so the slope will be negative. Now we know the slope is -1/3. The equation now that we figured out the slope is y = -1/3x + 5.
I hope this helps you! Let me know if I got something wrong.
