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Determinants
So the area of the parallelogram formed by the two vectors =
magnitude of the vector -13*i - 5*j - 6*k =
square root of (13^2 + 5^2 + 6^2) =
approximately 15.17
This shows how to find the determinant of a matrix and find the area of the parallelogram
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Vectors : Area of Parallelogram, Perpendicular Vectors , Angles Between Vectors, Orthogonal Vectors and Determinants
The cross-product u x v is perpendicular to both u and v.
b. The determinant of a 2x2 matrix is a vector.
c. The determinant of a 3x3 matrix is zero if two rows of the matrix are parallel vectors in .
d.
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Maple TA: Calculating an Angle, and the Area
alpha)
For e), it is based on the dot-product of the vectors a and b
Q2 (a) and (f)
For (a), as the module of the cross product of a and b is equal to the area of the parallelogram, which is |a||b|sin(alpha).
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Finding the Area of a Parallelogram
If A is actually (1, 2, 3), then the area of the parallelogram in 3-D is the length of the vector, which is the cross product of vector and
So
Therefore, the area is
If what you have is correct, then we have to calculate the area
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Area of Parallelogram Given Vertices
Solution:
First, we find two vectors that original from the same point. These two vectors represent the two adjacent sides of parallelogram. Let the point (3, 4) be the common point.
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Volume of a parallelepiped and vectors
The magnitude of the cross product of two vectors is equivalent to the area of the parallelogram they form, and the dot product is equivalent to the product of the projection of one vector onto another with the length of the vector projected upon.
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Altitude of a perallelepiped
340069 Altitude of parallelepiped Find the altitude of a parallelepiped determined by vectors A, B, and C if the base is taken to be the parallelogram determined by A and B and
A=i+j+k
B=2i+4j-k
C=i+j+3k.
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Using cross products to find orthogonal vectors and areas
Applying this formula, using the cross product we already worked out, we see that the area of the triangle PQR is |(6,3,2)|/2=7/2. One use of cross products is to find the area of triangles in 3D space.
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Area of the Parallelogram
Use this information to compute the area of the parallelogram generated by a_1=(1,0,1,0,1) and a_2=(1,1,1,1,1) in R^5. The solution is attached below in two files. the files are identical in content, only differ in format.