Projection of Vector (Jee Mains)

Vector Algebra and Components

Medium

Projection of Vector

Let (α, β, γ) be the co-ordinates of the foot of the perpendicular drawn from the point (5, 4, 2) on the line $\vec r = ( - \hat i + 3\hat j + \hat k) + \lambda (2\hat i + 3\hat j - \hat k).$
Then the length of the projection of the vector $\alpha \hat i + \beta \hat j + \gamma \hat k$ on the vector $6\hat i + 2\hat j + 3\hat k$ is :

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