Angle between two intersecting linesMedium

Intersection and Parallel Lines in Space

Let $\vec a = \hat i + 2\hat j + \hat k$ and $\vec b = 2\hat i + 7\hat j + 3\hat k$ . Let L₁: $\vec r = \left( { - \hat i + 2\hat j + \hat k} \right) + \lambda \vec a$ , λ ∈ R and L₂ : $\vec r = \left( {\hat j + \hat k} \right) + \mu \vec b$ , µ ∈ R, be two lines. If the line L₃ passes through the point of intersection of L₁ and L₂, and is parallel to $\vec a + \vec b$ , then L₃passes through the point:

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