Math Problem Statement
若向量 $\boldsymbol{a}$ 与 $\boldsymbol{b}$ 不共线则 ( ). A. $\boldsymbol{a}$ 与 $\boldsymbol{b}$ 均为非零向量 B. $\boldsymbol{a}$ 与 $\boldsymbol{b}$ 均为零向量 C. $\boldsymbol{a}$ 为零向量, $\boldsymbol{b}$ 为非零向量 D. $\boldsymbol{a}$ 为非零向量, $\boldsymbol{b}$ 为零向量
Solution
若向量 与 不共线,这意味着它们不在同一条直线上。因此,我们可以推断出以下结论:
- 如果向量 与 不共线,那么它们必须都是非零向量。如果其中任何一个向量是零向量,那么它们将是共线的,因为零向量可以看作在任何向量方向上的伸缩。
因此,正确的选项是:
A. 与 均为非零向量
Would you like more details or have any questions about this solution? Here are five more questions you might be interested in:
- How do you determine if two vectors are parallel?
- What is the geometric interpretation of vector addition?
- How do you find the dot product of two vectors?
- What is the cross product of two vectors and how is it used?
- How do you determine the angle between two vectors?
Tip: Understanding the properties of vectors, such as their direction and magnitude, is crucial in solving problems related to vector operations and their geometric interpretations.
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Math Problem Analysis
Mathematical Concepts
Vectors
Linear Algebra
Formulas
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Theorems
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Suitable Grade Level
Grades 11-12
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