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Dot product

21 practice questionsIntegral CalculusStep-by-step solutions

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1

For the mutually perpendicular unit vectors i,j,k\mathbf{i},\mathbf{j},\mathbf{k}, which statement is correct?

A.i⋅j=0\mathbf{i}\cdot\mathbf{j}=0, j⋅k=0\mathbf{j}\cdot\mathbf{k}=0, i⋅i=1\mathbf{i}\cdot\mathbf{i}=1
B.i⋅j=1\mathbf{i}\cdot\mathbf{j}=1, j⋅k=1\mathbf{j}\cdot\mathbf{k}=1, i⋅i=1\mathbf{i}\cdot\mathbf{i}=1
C.i⋅j=k\mathbf{i}\cdot\mathbf{j}=\mathbf{k}, j⋅k=i\mathbf{j}\cdot\mathbf{k}=\mathbf{i}, i⋅i=1\mathbf{i}\cdot\mathbf{i}=1
D.i⋅j=0\mathbf{i}\cdot\mathbf{j}=0, j⋅k=0\mathbf{j}\cdot\mathbf{k}=0, i⋅i=0\mathbf{i}\cdot\mathbf{i}=0
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2

What type of quantity is the result of a⋅b\mathbf{a}\cdot\mathbf{b}?

A.A scalar
B.A vector parallel to a\mathbf{a}
C.A vector perpendicular to both a\mathbf{a} and b\mathbf{b}
D.A unit vector
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3

A force F=10i+3j−4k\mathbf{F}=10\mathbf{i}+3\mathbf{j}-4\mathbf{k} N acts on a particle as it moves through displacement d=2i−3j+k\mathbf{d}=2\mathbf{i}-3\mathbf{j}+\mathbf{k} m. Calculate the work done.

A.77 J
B.−7-7 J
C.1717 J
D.(−9,−18,−36)(-9,-18,-36) J
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