If x and y are linearly independent vectors in ℝ 3 , then they can be used to form a parallelogram P in the plane through the origin corresponding to Span ( x , y ) . Show that Area of P = ‖ x × y ‖
If x and y are linearly independent vectors in ℝ 3 , then they can be used to form a parallelogram P in the plane through the origin corresponding to Span ( x , y ) . Show that Area of P = ‖ x × y ‖
Solution Summary: The author explains that if x and y are linearly independent vectors in R3, then they can be used to form a parallelogram P in the plane through the origin corresponding to
If x and y are linearly independent vectors in
ℝ
3
,
then they can be used to form a parallelogram P in the plane through the origin corresponding to
Span
(
x
,
y
)
.
Show that
Area
of
P
=
‖
x
×
y
‖
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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