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Engineering Calculus Notes 57

Engineering Calculus Notes 57 - 45 1.3 LINES IN SPACE(d...

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1.3. LINES IN SPACE 45 (d) Show that the intersection of B and C is given by s = β αβ + βγ + γα t = γ αβ + βγ + γα . (e) Conclude that all three lines meet at the point given by −→ p A p α αβ + βγ + γα P = −→ p B p β αβ + βγ + γα P = −→ p C p γ αβ + βγ + γα P = 1 αβ + βγ + γα ± βγ −→ a + γα −→ b + αβ −→ c ² . Challenge problem: 9. Barycentric Coordinates: Show that if −→ a , −→ b and −→ c are the position vectors of the vertices of a triangle ABC in R 3 , then the position vector v of every point P in that triangle (lying in the plane determined by the vertices) can be expressed as a linear combination of −→ a , −→ b and −→ c v = λ 1
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