Question 1301a

Vectors II: Lines and Planes
Vector Equation of a Line I

Question

Find the equation of the line passing through the point P(1,5,3){P \left( - 1, 5, - 3 \right)} and parallel to the vector (302).{\begin{pmatrix} 3 \\ 0 \\ 2 \end{pmatrix}.}

Attempt

l:{l: } r=a+λd,  λR.{\mathbf{r}=\mathbf{a}+\lambda\mathbf{d}, \; \lambda \in \mathbb{R}.}
a={\mathbf{a}=}
({\Biggl(}
),{\Biggr), \quad}
d={\mathbf{d}=}
({\Biggl(}
){\Biggr)}

Answer

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