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Questions and Answers
Which of the following is the rule for vector addition of two or more vectors according to the parallelogram law?
Which of the following is the rule for vector addition of two or more vectors according to the parallelogram law?
- Placing the vectors head to head and drawing the vector from the free head to the free tail
- Placing the vectors head to tail and drawing the vector from the free tail to the free head (correct)
- Placing the vectors head to head and drawing the vector from the free tail to the free head
- Placing the vectors head to tail and drawing the vector from the free head to the free tail
How can vector addition be performed in Cartesian coordinates?
How can vector addition be performed in Cartesian coordinates?
- By multiplying the corresponding components of the vectors
- By subtracting the corresponding components of the vectors
- By adding the corresponding components of the vectors (correct)
- By dividing the corresponding components of the vectors
What is the notation used in the Wolfram Language to indicate vector addition?
What is the notation used in the Wolfram Language to indicate vector addition?
- Multiplication sign
- Division sign
- Minus sign
- Plus sign (correct)
What is the sum of vectors $\mathbf{u} = \langle u_1, u_2 \rangle$ and $\mathbf{v} = \langle v_1, v_2 \rangle$?
What is the sum of vectors $\mathbf{u} = \langle u_1, u_2 \rangle$ and $\mathbf{v} = \langle v_1, v_2 \rangle$?
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What is the sum of vectors $\mathbf{a} = \langle a_1, a_2, ..., a_n \rangle$ and $\mathbf{b} = \langle b_1, b_2, ..., b_n \rangle$?
What is the sum of vectors $\mathbf{a} = \langle a_1, a_2, ..., a_n \rangle$ and $\mathbf{b} = \langle b_1, b_2, ..., b_n \rangle$?
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Study Notes
Vector Addition Rules
- According to the parallelogram law, when adding two or more vectors, the resultant vector is the diagonal of a parallelogram formed by the vectors being added.
Vector Addition in Cartesian Coordinates
- To add vectors in Cartesian coordinates, add corresponding components (x and y) separately.
Vector Addition Notation
- In the Wolfram Language, vector addition is indicated by the
+operator.
Sum of Vectors
- The sum of vectors u = 〈u1, u2〉 and v = 〈v1, v2〉 is 〈u1 + v1, u2 + v2〉.
- The sum of vectors a = 〈a1, a2, ..., an〉 and b = 〈b1, b2, ..., bn〉 is 〈a1 + b1, a2 + b2, ..., an + bn〉.
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