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Find the Vectors u+v\mathbf { u } + \mathbf { v }

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Find the vectors u+v\mathbf { u } + \mathbf { v } , uv\mathbf { u } - \mathbf { v } , and 3u12v3 \mathbf { u } - \frac { 1 } { 2 } \mathbf { v } . u=a,2b,3c,v=a,b,2c\mathbf { u } = \langle a , 2 b , 3 c \rangle , \mathbf { v } = \langle - a , b , - 2 c \rangle


Definitions:

Transparent

A material's ability to allow light to pass through it so that objects behind can be distinctly seen.

Hardness

A measure of how resistant a material is to deformation, scratching, or penetration.

Fractures

Breaks or cracks in rock or bone, often resulting from stress or impact.

Sulfide Mineral

A mineral compound characterized by the presence of sulfur in combination with metals such as iron, copper, or zinc.

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