Vector Dot Product Learning Goal: To understand the rules for computing dot products. Let vectors A(2,1,4),B=(−3,0,1),C=(−1,−1,2) Dot product of a vector and a scalar? Which of the following can be computed? Which of the following can be computed? a) A―⋅B―⋅C― b) A―⋅(B⋅C―) c) A―⋅(B―+C―) d) 3A―

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Vector Dot Product Learning Goal: To understand the rules for computing dot products. Let vectors A(2,1,4),B=(−3,0,1),C=(−1,−1,2)  Dot product of a vector and a scalar? Which of the following can be computed? Which of the following can be computed?  a) A―⋅B―⋅C―  b) A―⋅(B⋅C―)   c) A―⋅(B―+C―)  d) 3A―

kalupunangh · Accepted Answer

Dot product of scalar and vector is not defined.  1. A―⋅B―⋅C―  This cannot be computed as dot product of any 2 vectors gives scalar.  Then dot product of scalar and other vector is not defined.  2. A―⋅(B―⋅C―)  This cannot be computed as dot product of B― and C― is scalar.  Then dot product of  A― and scalar is not defined.  3. A―⋅(B―+C―)  This can be computed.  A―⋅(B―+C―)=(2,1,−4)⋅((−3),0,1)+(−1,−1,2))  ∴A―⋅(B―+C―)=(2,1,−4)⋅(−4,−1,3)  ∴A―⋅(B―+C―)=(2×(−4))+(1×(−1))+(−4×3)  ∴A―⋅(B―+C―)=−8−1−12  ∴A―⋅(B―+C―)=−21  4. This cannot be computed as dot product of scalar and other vector is not defined.

Thomas Lynn · Accepted Answer

Can you please explain in text, without numbers?

nick1337 · Accepted Answer

The dot product can only take on two vectors. The dot product gives a scalar value.  In (a) the dot product between first two vector gives a scalar and the third vector cannot be taken further for a dot product with the scalar value. Hence the equation is not computable.  In (b) the dot product between last two vector gives a scalar and the first vector cannot be taken further for a dot product with the scalar value. Hence the equation is not computable.  In ( c) the addition between last two vector gives a vector and the first vector can be taken further for a dot product with the sum of last two vectors. Hence the equation is computable.  In (d) 3 is a scalar, hence the vector image cannot undergo dot product with the scar. The equation is not computable.  The operation which is computable is ( c) image.

Vector Dot Product Learning Goal: To understand the rules for

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