The parallelogram shown here has vertices at A(2, -1, 4),

Chapter , Problem 62PE

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The parallelogram shown here has vertices at $A(2, -1, 4)$, $B(1, 0, -1)$, $C(1, 2, 3)$, and $D$. Find

a. the coordinates of $D$,

b. the cosine of the interior angle at $B$,

c. the vector projection of $\overrightarrow{B A}$ onto $\overrightarrow{B C}$.

d. the area of the parallelogram,

e. an equation for the plane of the parallelogram,

f. the areas of the orthogonal projections of the parallelogram on the three coordinate planes.

Equation Transcription:

$A(2,-1,4)$

$B(1,0,-2)$

$C(1,2,3)$

$D$

$B$

$\vec{BA}$

$\vec{BC}$

Text Transcription:

A(2,-1,4)

B(1,0,-2)

C(1,2,3)

^overrightarrow BA

^overrightarrow BC

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