Alternatively, using formula for perpendicular component magnitude:
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- \mathbf{v}_{\perp} = egin{pmatrix} 2 \ -1 \ 3 \end{pmatrix} - egin{pmatrix} -0.5 \ -1 \ 0.5 \end{pmatrix} = egin{pmatrix} 2.5 \ 0 \ 2.5 \end{pmatrix}
- The magnitude of the perpendicular component (which is the desired quantity for speed component):
- \|\mathbf{v}_{\perp}\| = \sqrt{(2.5)^2 + 0^2 + (2.5)^2} = \sqrt{6.25 + 6.25} = \sqrt{12.5} = rac{5\sqrt{2}}{2}
- \|\mathbf{v}_{\perp}\| = \sqrt{\|\mathbf{v}\|^2 - \left( rac{|\mathbf{v} \cdot \mathbf{c}|}{\|\mathbf{c}\|}
- But since we already computed it:
- oxed{\dfrac{5\sqrt{2}}{2}}
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