Question 1301b

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

Question

Find the equation of the line that is parallel to
l2:r=(5−1−2)+μ(3−10),  μ∈Rl_2: \mathbf{r} = \begin{pmatrix} 5 \\ - 1 \\ - 2 \end{pmatrix} + \mu \begin{pmatrix} 3 \\ - 1 \\ 0 \end{pmatrix}, \; \mu \in \mathbb{R}
and passes through the point P(4,1,2).{P \left( 4, 1, 2 \right).}

Attempt

l:{l: } r=a+λd,  λ∈R.{\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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