What's the vector form of the line going through this point?
P = (1, 1, 2), Q = (-1, 0, 3), R = (2, 1, -1).
Line passes through (1, 1, 2) and is perpendicular to the triangle made by these three points. What's the vector form of this line?
P = (1, 1, 2), Q = (-1, 0, 3), R = (2, 1, -1).
Line passes through (1, 1, 2) and is perpendicular to the triangle made by these three points. What's the vector form of this line?
2 Answers
Explanation:
The reqd. line
Clearly, the direction
plane
We take,
Thus, we see that
direction
Hence, the vector eqn. of
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Explanation:
The plane containing the triangle is
where only the ratio
Adding first two,
Twice the second plus the third,
Subtracting,
Substituting,
WLOG let
Check:
So the normal vector to this plane is
Some teachers like the equivalent form with unit vectors: