- #1

lolimcool

- 20

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## Homework Statement

P is the point where the diagonals of the parallelogram abcd intersect one another

let [itex]\alpha = AB[/itex] and [itex]\beta = AD[/itex] and let s and t be scalars such that [itex]AP = sAC[/itex] and [itex]BP = tBD[/itex]

use vector algebra to show that

[itex]s(\alpha + \beta) = AP = \alpha + t(\beta - \alpha)[/itex]

## The Attempt at a Solution

ok so

s(AB + AD) = AP = AB + t(AD - AB)

s(AC) = AP = AB + t(BD) (s(AC) and AP have the same direction so s(AC) = AP)

AP = AB + t(BD)

AP = AB + BP

AP = AP

is that right?and could someone explain to me the principle of planar independence