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Vectors and Euclidean Space
Vector arithmetic, the dot and cross products, projections, and the geometry of lines and planes.
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The scalar projection of
u
\mathbf{u}
u
onto a nonzero
v
\mathbf{v}
v
is defined as:
Review the explanation for this topic →
u
⋅
v
∥
v
∥
\dfrac{\mathbf{u}\cdot\mathbf{v}}{\|\mathbf{v}\|}
∥
v
∥
u
⋅
v
u
⋅
v
∥
v
∥
2
v
\dfrac{\mathbf{u}\cdot\mathbf{v}}{\|\mathbf{v}\|^2}\mathbf{v}
∥
v
∥
2
u
⋅
v
v
u
⋅
v
∥
u
∥
\dfrac{\mathbf{u}\cdot\mathbf{v}}{\|\mathbf{u}\|}
∥
u
∥
u
⋅
v
∥
u
∥
∥
v
∥
cos
θ
\|\mathbf{u}\|\,\|\mathbf{v}\|\cos\theta
∥
u
∥
∥
v
∥
cos
θ
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