Fundamentals of Chemical Engineering: [One Question per Day] 2010-12-01
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This post was last edited by sailan on 2010-12-2 09:00. 1. Explain the difference between the scalar product and vector product of vectors. 2. Which of the following substances can form hydrogen bonds: HCl, H3BO3, CH3OH, H2S, NH3, PH3, H3PO4. Note: 1) All participants will receive a reward; those who provide detailed calculation processes will get 10–15 wealth points or 1 charm point. 2) Please hide your replies. Do not edit them after posting, and also do not copy others’ answers, as that will result in a deduction of points. 3) The reference answers will be released early tomorrow morning; students who want to check their answers are welcome to come and take a look. 4) Please also avoid submitting answers multiple times maliciously. If it is due to an operational error, please contact the forum moderators or administrators; otherwise points will be deducted. If you have any questions, you can refer to Keke’s answer on floor 18.
The dot product of vectors is the numerical product; the result of the dot product of vector quantities is a vector. In terms of the right-hand rule, this involves the components of the vectors. H3BO3, CH3OH, NH3, H3PO4
1. The dot product of vectors is the numerical product, and the result is a scalar. The cross product of vectors is the vector sum of the vectors according to the right-hand rule. 2. CH3OH
1: Unclear 2: NH3 can form hydrogen bonds; check the answer
Reply 1# sailan: The dot product is a number, while the cross product is a vector. H3BO3 CH3OH H3PO4
1. The dot product of vectors is the product of a number and a vector, and the result is a vector； The vector product, on the other hand, is the product of two vectors, and the result is a number. 2. HCl, NH3, PH3, HS2
1. The scalar product of vectors is the numerical product, and the result is a scalar; the vector product of vectors is the vector sum of the components according to the right-hand rule. 2. Can form hydrogen bonds: HCl, H3BO3, CH3OH, HS2, NH3, PH3
1. Scalar product: The product of the magnitudes of two vectors a and b and the cosine of the angle between them. It is also called the dot product. Vector dot product: Vector c is given by vectors a and b as follows: the magnitude of c is equal to the product of the magnitudes of a and b, multiplied by the sine of the angle between vectors a and b ； c is perpendicular to both ab and satisfies the right-hand rule. 2. H3BO3, CH3OH, HS2, NH3, PH3, H3PO4
1. Vector product: Also known as the scalar product, cross product, or external product, it is a binary operation on vectors in a vector space. Unlike the dot product, its result is a pseudovector rather than a scalar. And the cross product of the two vectors is perpendicular to both of them. The magnitude of the cross product, |a × b|, can be interpreted as the area of the parallelogram with sides a and b. The scalar product: also known as the “inner product” or “dot product,” it is referred to as a “scalar product” in physics. The dot product of the two vectors a and b is the quantity |a|·|b|cosθ, denoted as a·b ； Here, |a| and |b| are the magnitudes of the two vectors, and θ is the angle between the two vectors (0≤θ≤π). That is, given two non-zero vectors a and b with an angle θ between them, the quantity |a||b|cosθ is called the dot product of a and b, denoted as a·b. 2, HCl, H3BO3, CH3OH, NH3, H3PO4 – these substances have hydrogen bonds
Reply 1# sailan: The dot product of two vectors is the numerical product, and the result is a scalar. The cross product of vectors is the vector sum of the components of those vectors according to the right-hand rule. 2. NH3 HCL