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# Precalculus MM: Lair of the Devourer: Vectors and Parametric Equations 3: NWN 0140b

Such is the nobility of Daelan's words that the pride Zanzi feels in him for uttering them brings a lump to her throat, but she still believes the henchman's sense of honour is preventing him from fully appreciating what "extremely unpleasant" means in this context. So at first she does not speak her response but gently touches his arm as a gesture acknowledging the import of his words. Then, to reassure Daelan, she tells him, "I'll not hesitate to use the Stone of Recall should either of us succumb to any of the creature's attacks." Zanzi then phases Daelan and herself with a stirring Bard Song, casts Invisibility on herself and walks with him through the doorway towards the lair of the devourer.
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After Zanzi rose to her feet she walked in a straight line towards the north exit of the room; as she did so the Stone of Recall used the vector equation of a line, r = r subzero + tv, to record her movements relative to the Hall of Justice portal (effectively the origin). In r = r subzero + tv, r represents the location of any point on the straight line as determined by the direction vector v and can be written in component form as position vector < x, y >; r subzero is the point whose components are obtained by starting at the origin and ending at the initial position vector < x subzero, y subzero > (i.e. in this instance where Zanzi rose from resting relative to the Hall of Justice portal); t is a scalar multiplier and v is the direction vector, namely the vector pointing to a second point which determines the gradient and direction of the straight line.
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The vector equation of a line is used to find any point on a straight line when the coordinates of a point and the coordinates of a direction vector to another point are known (or can be obtained from a known gradient), so there are similarities between this equation and the point slope form equation of a straight line, which is used when the coordinates of a point and slope ratio of a line are known. When studying the point slope form Zanzi obtained her first potion of Cure Serious Wounds, which she would rely on to save herself from an overpowering opponent. And in a similar way, she is relying on the Stone of Recall to save herself and her henchman should either succumb to the psionic powers of the intellect devourer.
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