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Scalar triple product

14 practice questionsIntegral CalculusStep-by-step solutions

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1

Find the volume of the parallelepiped with edges a=2i\mathbf{a}=2\mathbf{i}, b=3j\mathbf{b}=3\mathbf{j}, c=i+j+4k\mathbf{c}=\mathbf{i}+\mathbf{j}+4\mathbf{k}, meeting at a common vertex.

A.2424
B.1212
C.66
D.7272
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2

What does the scalar triple product aโ‹…(bร—c)\mathbf{a}\cdot(\mathbf{b}\times\mathbf{c}) represent geometrically when a,b,c\mathbf{a},\mathbf{b},\mathbf{c} are edges of a parallelepiped meeting at one vertex?

A.Its absolute value equals the volume of the parallelepiped
B.Its absolute value equals the surface area of the parallelepiped
C.It always equals zero for any parallelepiped
D.Its absolute value equals half the volume of the parallelepiped
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3

Show whether a=i+j\mathbf{a}=\mathbf{i}+\mathbf{j}, b=j+k\mathbf{b}=\mathbf{j}+\mathbf{k}, c=i+2j+k\mathbf{c}=\mathbf{i}+2\mathbf{j}+\mathbf{k} are coplanar, by computing aโ‹…(bร—c)\mathbf{a}\cdot(\mathbf{b}\times\mathbf{c}).

A.00, so the vectors are coplanar
B.22, so the vectors are not coplanar
C.โˆ’1-1, so the vectors are not coplanar
D.11, so the vectors are coplanar
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