ausmathgenius420
New member
- Joined
- Aug 5, 2021
- Messages
- 44
Hi,
My textbook asks the question:
Find a Cartesian equation of the plane that is at right angles to the line given by x = 4 + t, y = 1 − 2t, z = 8t and goes through the point P(3, 2, 1).
For simplicity I will convert to vector form...
1. Convert to vector form
[math]r=(4+t)i +(1-2t)j+8tk[/math][math]4i+j+t(i-2j+8k)[/math]
Therefore the line travels in a direction of [imath]i-2j+8k[/imath]
Looking at the textbooks solution, they then conclude that the normal vector is also [imath]i-2j+8k[/imath]
Can someone explain why this is true?
My textbook asks the question:
Find a Cartesian equation of the plane that is at right angles to the line given by x = 4 + t, y = 1 − 2t, z = 8t and goes through the point P(3, 2, 1).
For simplicity I will convert to vector form...
1. Convert to vector form
[math]r=(4+t)i +(1-2t)j+8tk[/math][math]4i+j+t(i-2j+8k)[/math]
Therefore the line travels in a direction of [imath]i-2j+8k[/imath]
Looking at the textbooks solution, they then conclude that the normal vector is also [imath]i-2j+8k[/imath]
Can someone explain why this is true?