Expressing a Vector Line Equation

00:00 3 marks

Find the vector equation of the line that passes through the point \(A(1, -2, 3)\) and is parallel to the vector \(\vec{v} = \langle 4, 0, -5 \rangle\). Express your answer in the form \(\vec{r} = \vec{r}_0 + t\vec{v}\), where \(t\) is a real number.

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Hint

Recall that the vector equation of a line can be written as \(\vec{r} = \vec{r}_0 + t\vec{v}\).

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\(\vec{r} = \langle 1, -2, 3 \rangle + t\langle 4, 0, -5 \rangle\)

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Expressing a Vector Line Equation

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Expressing a Vector Line Equation

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