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Engineering Calculus Notes 100

Engineering Calculus Notes 100 - 88 CHAPTER 1 COORDINATES...

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88 CHAPTER 1. COORDINATES AND VECTORS Similarly, a 1 −→ ı = 2 vector A ( △O P 1 Q 1 ) = −→ ı vextendsingle vextendsingle vextendsingle vextendsingle y 1 z 1 y 2 z 2 vextendsingle vextendsingle vextendsingle vextendsingle . Finally, noting that the direction from which the positive z -axis is counterclockwise from the positive x -axis is −→ , we have a 2 −→ = 2 vector A ( △O P 2 Q 2 ) = −→ vextendsingle vextendsingle vextendsingle vextendsingle x 1 z 1 x 2 z 2 vextendsingle vextendsingle vextendsingle vextendsingle . Adding these yields the desired formula. In each projection, we used the 2 × 2 determinant obtained by omitting the coordinate along whose axis we were projecting. The resulting formula can be summarized in terms of the array of coordinates of −→ v and −→ w parenleftbigg x 1 y 1 z 1 x 2 y 2 z 2 parenrightbigg by saying: the coefficient of the standard basis vector in a given coordinate direction is the 2 × 2 determinant obtained by eliminating the corresponding column from the above array, and multiplying by
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