Vector Projection onto Another Vector (Jee Mains)

Vector Algebra and Components

Medium

Vector Projection onto Another Vector

Let $\overrightarrow a = 2\hat i - \hat j - \hat k,\overrightarrow b = \hat i + 3\hat j - \hat k$ and $\overrightarrow c = 2\hat i + \hat j + 3\hat k$ . Let $\overrightarrow v$ be the vector in the plane of the vectors $\overrightarrow a$ and $\overrightarrow b$ such that the length of its projection on the vector $\overrightarrow c$ is $\frac{1}{{\sqrt {14} }}$ . Then $\left| {\overrightarrow \nu } \right|$ is equal to

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