Find a unit vector with positive first coordinate that is orthogonal to the plane through the...
Question:
Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P(-3,-2,3), Q(-1,0,5) and R(-1,0,10)
Unit Vector Orthogonal to a Plane:
To find a normal vector to a plane (say {eq}A {/eq}) that passes through three points, we first find two vectors parallel to the plane {eq}A {/eq} using the three given points.
The cross-product of the two vectors found above provides a normal to the plane {eq}A {/eq}.
The unit vector in the direction of the normal vector is found by dividing the normal vector by its magnitude.
Answer and Explanation: 1
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View this answerAnswer: {eq}\dfrac {\langle 1,\,-1,\, 0\rangle}{\sqrt{2}} {/eq}
Explanation: Denote the plane containing the three given points as plane A. Two...
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