Vector projection of $$$\left\langle 1, 0, 1\right\rangle$$$ onto $$$\left\langle 0, 3, 4\right\rangle$$$
Related calculator: Scalar Projection Calculator
Your Input
Calculate the vector projection of $$$\mathbf{\vec{v}} = \left\langle 1, 0, 1\right\rangle$$$ onto $$$\mathbf{\vec{u}} = \left\langle 0, 3, 4\right\rangle$$$.
Solution
The vector projection is given by $$$\operatorname{proj}_{\mathbf{\vec{u}}}\left(\mathbf{\vec{v}}\right) = \frac{\mathbf{\vec{v}}\cdot \mathbf{\vec{u}}}{\mathbf{\left\lvert\vec{u}\right\rvert}^{2}} \mathbf{\vec{u}}.$$$
$$$\mathbf{\vec{v}}\cdot \mathbf{\vec{u}} = 4$$$ (for steps, see dot product calculator).
$$$\mathbf{\left\lvert\vec{u}\right\rvert} = 5$$$ (for steps, see vector magnitude calculator).
Thus, the vector projection is $$$\operatorname{proj}_{\mathbf{\vec{u}}}\left(\mathbf{\vec{v}}\right) = \frac{4}{5^{2}}\cdot \left\langle 0, 3, 4\right\rangle = \frac{4}{25}\cdot \left\langle 0, 3, 4\right\rangle = \left\langle 0, \frac{12}{25}, \frac{16}{25}\right\rangle$$$ (for steps, see vector scalar multiplication calculator).
Answer
The vector projection is $$$\left\langle 0, \frac{12}{25}, \frac{16}{25}\right\rangle = \left\langle 0, 0.48, 0.64\right\rangle$$$A.