Vector calculus in plane and space: Vectors in Planes and Space
Addition of vectors
Let #\vec{u}#, #\vec{v}#, and #\vec{w}# be three vectors. Write the linear combination #(7\vec{u}+3\vec{v}+4\vec{w}) + (-7\vec{u} + 2\vec{v} +\vec{w})# in such a way that the three vectors each appear once with an integer scalar.
#(7\vec{u}+3\vec{v}+4\vec{w}) + (-7\vec{u} + 2\vec{v} +\vec{w})=# #\cdot\vec{u}# #+# #\cdot\vec{v}# #+# #\cdot\vec{w}#
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