The vector cross product (2i + 6j + 27k) × (i + pj + qk) = 0 implies that the two vectors are parallel. For the cross product to be zero, the components must satisfy the condition: 2p + 6q ...
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A square matrix is a matrix with an equal number of rows and columns. The order of a square matrix refers to its size, represented as “n x n,” where “n” is the number of rows (or columns). Examples include ...
Elongation is the increase in length of a material when subjected to tensile stress. It is a measure of how much a material stretches under load and is typically expressed as a percentage of the original length. Elongation is crucial ...
Elastic materials can regain their original shape and size after the removal of an applied force. This property allows them to undergo reversible deformation without permanent change. Elasticity is crucial in various applications such as springs and rubber bands where ...
Modulus refers to a measure of a material’s stiffness or resistance to deformation under stress. It quantifies the relationship between stress and strain in elastic materials. Common types include Young’s modulus for tensile stress shear modulus for shear stress and ...
Cross-sectional refers to the shape or area obtained by cutting through an object perpendicular to its longest dimension. It provides insights into the internal structure and characteristics of the material. In engineering and physics cross-sectional analysis is crucial for understanding ...
A ratio is a mathematical expression that compares two quantities by division. It shows the relative sizes of two or more values and can be represented in various forms such as fractions decimals or percentages. Ratios are commonly used in ...
To derive means to obtain or develop a result or conclusion from existing knowledge or principles through logical reasoning and calculations. In mathematics and physics it often involves formulating equations or formulas based on fundamental laws and relationships. Derivation is ...
Elasticity is the property of a material to return to its original shape and size after the removal of an applied force. It allows materials to undergo temporary deformation without permanent change. Elastic behavior is crucial in applications such as ...
Elastic hysteresis refers to the phenomenon where a material experiences a difference in its stress-strain behavior during loading and unloading cycles. When a material is stretched and then released the energy absorbed during deformation is not entirely recovered resulting in ...