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=(4−23)+μ(−552),  μ∈Rl_2: \mathbf{r} = \begin{pmatrix} 4 \\ - 2 \\ 3 \end{pmatrix} + \mu \begin{pmatrix} - 5 \\ 5 \\ 2 \end{pmatrix}, \; \mu \in \mathbb{R}
and passes through the point P(−3,−5,−4).{P \left( - 3, - 5, - 4 \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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